View Full Version : The problem with aging stars


7shadesofblack
09-15-2007, 05:39 PM
I've wondered sometimes, and there are plenty of examples to look at, if the reason that many aging musicians/rockstars fail to match their earlier genius is because they have little memory or memories distorted by time of what it is like to be an average person.
In Billy's case, I'm certainly not one of the Zeit haters, and I think it's a worthwhile record, but it cannot be favorably compared with his first 3 LP's. Why is that? There are tons of variables, and I'm sure it's a combination of them, but the one I'd like to hear your opinion of is the possibility of rockstardom's corrupting nature.
It would probably be tough to write meaningful, authentic songs that the masses can relate to when for the last 15 or more years you've either been on world tours, crammed onto a bus, living as a recluse in your mansion, unsuccessfully dating other stars/"artists", and working in the studio. That's not much of a life at all. It's easy to think a life like that would be awesome, and it probably would for some time, but has it erased Billy's notions of himself and the world? For his first three albums it seems he was writing on behalf of a poor kid from Chicago, taken for granted, abused, bright, angry, romantic...and having read his confessions, he lead a strange life, mingling with homeless hookers in Florida while his first band went no where and he ran out of money. All of that stuff is great material, and when he was writing from that perspective I think he wrote many of the best songs from the 90's, period.
But it seems that eventually he made the conscious decision (the point at which he made it is debatable) that it was time to "grow up" and write songs from his then-current point of view, and that's when his songs lifted off and have never touched earth again. Most of his songs ever since have, although musically impressive, been at best lofty, and at worst contrived. I don't necessarily say that as an insult, and that's the point of my thread.
In between SP1 and SP2 instead of dabbling with Zwan and electronic music experiments, I wish he could have disappeared in the witness protection program, worked a standard job, met actual girls that still have souls, gone on some vacations, and lived as most average people do...then when it was time for SP2 maybe we would have some songs with the punch and depth of Rhinoceros, Spaceboy, Hummer, To Forgive and so on.
Obviously that scenario is unrealistic on several levels, but do you people agree or disagree with this idea? Have some examples of other musicians that support or are exceptions to my theory?

dasuitekilla
09-15-2007, 05:45 PM
ban

7shadesofblack
09-15-2007, 05:48 PM
ban

damnit, don't ban me. If you decipher that long, phony analysis it's actually just code for "Dude, have yall noticed how sweet Ginger's ass is?"

exactlythesame
09-15-2007, 05:51 PM
there's no lack of musicians whom this theory can apply to.

it almost goes without saying that rock stardom does affect your worldview, though it's debatable whether it's in a good way or a bad way.

i don't feel like there are any songs on zeitgeist i can even closely relate to, though i appreciate that they must mean something to the artist who wrote them. however, it doesn't mean that they're bad or anything. part of the reason i listen to music is that it gives me a doorway into other people's lives and feelings, and lets me see their own world as they see it. i may not agree or even understand their viewpoints, but most of the time it's interesting and entertaining (depending, of course, upon who you choose to listen to.)

you bring up several good ideas, though, so thanks for sharing. gives me something to read on a saturday afternoon.

I Don't Live
09-15-2007, 05:56 PM
ban
What do u contribute here?

ChaosEffect
09-15-2007, 06:02 PM
You mean the problem with aging StarZ right?

7shadesofblack
09-15-2007, 06:08 PM
You mean the problem with aging StarZ right?

Haha yes of course.

skipgo
09-15-2007, 06:17 PM
i think you bring up some very valid points. I'd like to add something to it, but i've been doing yard work most of the day and i'm beat. I just wanted to let you know that I think you're theory is pretty interesting, and there's quite likely something to it. There are very few famous people who's art hasn't been affected in a negative way by said fame. However, even if Billy WERE able to go through life incognito for a while, he'd still never live a "normal" life, because he'd know what was waiting for him when he came back; fame, money, all that. He'd have to lose everything and not expect to get it back before he could experience life like one of us again. And even then, it would probably take a long time to get used to the idea that he wasn't a wealthy rockstar. Meaning, we'll probably never hear that same level of emotion from this band again. :(

TAFH
09-15-2007, 06:21 PM
probably the only reasonable post I've read on this forum of idiots.

I think you made a great point. Billy has been incapable of achieving depth in his music for quite a long time. I personally don't like anything after Adore, even though I don't like Adore too much, it doesn't hurt to hear, and it doesn't make me feel embarrassed of the fact that I was once a fan of bill.

Zeitgeist not only proved that bill has no connection with anyone anymore, also it proved that bill's a sellout. He's using politics to sell and the album's political content is laughable. It only shows how little he knows.

Anyhow, if your "theory" is true, then, it means he'll never produce anything good again... how about that ?

monkeyfritters
09-15-2007, 06:24 PM
good thread... I agree zeitgeist sucks and corgan has lost it.

exactlythesame
09-15-2007, 06:24 PM
isn't that what every thread on here is about

monkeyfritters
09-15-2007, 06:25 PM
hope so.

7shadesofblack
09-15-2007, 06:34 PM
Well, even if my theory is true, Zeitgeist is still a good album, better than many that outsold it and won wide acclaim among the critics. That's because Billy is still a virtuoso with the guitar, and a good songwriter in general.

Schnobja
09-15-2007, 06:56 PM
I don't know. It's an interesting theory but I'm inclined to disagree because Billy was able to write Adore after hitting it big with MCIS.

pete
09-15-2007, 07:02 PM
That was actually one of the most coherant and interesting things I've ever read on this board. Especially the part about 'at best lofty, at worst contrived'...sums it up very well.

bampton
09-15-2007, 07:18 PM
Billy is still a virtuoso with the guitar

Bill was never, and never will be a virtuoso with the guitar. Sure, he's not bad, he's pretty cretive and pretty good at what he does, but he's no virtuoso.

Apart from that, this has been a good thread.

sweetanthony
09-15-2007, 07:24 PM
That was actually one of the most coherant and interesting things I've ever read on this board. Especially the part about 'at best lofty, at worst contrived'...sums it up very well.

My thoughts exactly, but I still seem to find that a point made earlier about how he did write Adore after quite a bit of years of large success... but, he had major life-changing events occur, i.e. his mother died, Jimmy OD/Melvoin death, Yelena, and MEGA-stardom (different from SD-era success). So, even though stardom of sorts, distorts his perspective and alters his connection with us, there will still be events in his life that in some way are relatable with us.

Who knows, Bill Sr. might die before the next album and we'll get the best rock record of all-time. :erm:

pete
09-15-2007, 07:27 PM
relatable with us.

Who knows, Bill Sr. might die before the next album and we'll get the best rock record of all-time. :erm:

You're not the first to suggest that im sad to say...it even got it own thread for fucks sake.

pumpkinxyu
09-15-2007, 07:31 PM
while i don't think there's a total lack of validity in the original poster's theory, i think the argument could be reversed to point fingers at a lot of the fans. while you can say that billy can't relate to what it's like to be just a "regular" person anymore, you could also say that the man has traveled the world, been completely embraced by an entire international culture, been greatly rejected by much of said culture, played with his heroes from when he was just a regular guy, fallen in love [yelena], lost his musical soulmate to drugs, reconnected with his musical soulmate, lost two of his closest friends as they differed in their reaction to these experiences, and on and on and on...

in short, i'd say he's lived a pretty fantastic life. he's done great things with his limited amount of time on earth, made possible by his bold decisions, his dedication, and his work ethic. so rather than saying his music isn't as good now because he's too detached from reality and lacks depth, maybe the people who don't like his last several albums are lacking in depth because they can't think outside of their own smaller day-to-day experiences at mundane jobs in a largely status quo environment. the assumption is that billy's vast wealth of experience detracts from his ability to write while those of us sitting on the internet are constantly broadening our horizons. i know suburbia has been the breeding ground for a lot of "depth" in rock music, but i'd say that music doesn't necessarily suffer from these larger-than-life experiences. and there are plenty of examples of artists who have made their best work almost as a response to this detachment from the average-joe lifestyle: the Beatles, Pink Floyd, David Bowie, Led Zeppelin, Radiohead, U2, R.E.M., etc.

that's not to say that a lot of these bands didn't eventually end up making crappy music (the Beatles, Radiohead, and U2 being the exceptions for me). i feel like most artists do go south beyond a certain age, as billy said in that XM Live interview. but not necessarily for the reasons stated in this thread. it has a lot to do with mentality. once you see yourself as a novelty act, and you go out on stage to put on your pony show, it's over. unless there's some element of progression and danger in what you set out to do, then it's done and you can still sell t-shirts, but the heart of the band is gone.

billy is trying to re-establish the heart of the band with this album while still seeking new ground. it's a bit of a new balancing act for him, but i think he's doing it for the right reasons. he's perceptive enough to stay far enough away from novelty status to avoid its perils. anyone who's seen the band live this year knows that this does not feel like a reunion tour. these are intense concerts with a lot of new music. this isn't a couple of fat people wheezing through their back catalogue (sorry, pixies, but come on). i think Zeitgeist is a great record, and a very important record, although i can't say i've talked to many other people who feel very strongly about it. it stands up to the rest of the band's catalogue, i think. that's not to say anyone is supposed to like it, or even that anyone should go out of their way to relate to it, but i feel like billy's still going above and beyond in his role as a heartfelt writer and performer, and as long as he's doing that, the pumpkins will remain the best band in the world.

7shadesofblack
09-15-2007, 07:32 PM
I don't know. It's an interesting theory but I'm inclined to disagree because Billy was able to write Adore after hitting it big with MCIS.


In my opinion this album represents the crossroads, as such, in his career. The album seems to contain songs with the same gritty, earnestness of his early records, but also some that depart into the territory he has been stuck in from that point onward.

7shadesofblack
09-15-2007, 07:43 PM
while i don't think there's a total lack of validity in the original poster's theory, i think the argument could be reversed to point fingers at a lot of the fans. while you can say that billy can't relate to what it's like to be just a "regular" person anymore, you could also say that the man has traveled the world, been completely embraced by an entire international culture, been greatly rejected by much of said culture, played with his heroes from when he was just a regular guy, fallen in love [yelena], lost his musical soulmate to drugs, reconnected with his musical soulmate, lost two of his closest friends as they differed in their reaction to these experiences, and on and on and on...

in short, i'd say he's lived a pretty fantastic life. he's done great things with his limited amount of time on earth, made possible by his bold decisions, his dedication, and his work ethic. so rather than saying his music isn't as good now because he's too detached from reality and lacks depth, maybe the people who don't like his last several albums are lacking in depth because they can't think outside of their own smaller day-to-day experiences at mundane jobs in a largely status quo environment. the assumption is that billy's vast wealth of experience detracts from his ability to write while those of us sitting on the internet are constantly broadening our horizons. i know suburbia has been the breeding ground for a lot of "depth" in rock music, but i'd say that music doesn't necessarily suffer from these larger-than-life experiences. and there are plenty of examples of artists who have made their best work almost as a response to this detachment from the average-joe lifestyle: the Beatles, Pink Floyd, David Bowie, Led Zeppelin, Radiohead, U2, R.E.M., etc.

that's not to say that a lot of these bands didn't eventually end up making crappy music (the Beatles, Radiohead, and U2 being the exceptions for me). i feel like most artists do go south beyond a certain age, as billy said in that XM Live interview. but not necessarily for the reasons stated in this thread. it has a lot to do with mentality. once you see yourself as a novelty act, and you go out on stage to put on your pony show, it's over. unless there's some element of progression and danger in what you set out to do, then it's done and you can still sell t-shirts, but the heart of the band is gone.

billy is trying to re-establish the heart of the band with this album while still seeking new ground. it's a bit of a new balancing act for him, but i think he's doing it for the right reasons. he's perceptive enough to stay far enough away from novelty status to avoid its perils. anyone who's seen the band live this year knows that this does not feel like a reunion tour. these are intense concerts with a lot of new music. this isn't a couple of fat people wheezing through their back catalogue (sorry, pixies, but come on). i think Zeitgeist is a great record, and a very important record, although i can't say i've talked to many other people who feel very strongly about it. it stands up to the rest of the band's catalogue, i think. that's not to say anyone is supposed to like it, or even that anyone should go out of their way to relate to it, but i feel like billy's still going above and beyond in his role as a heartfelt writer and performer, and as long as he's doing that, the pumpkins will remain the best band in the world.

Well, that is the direct opposite of my theory, and I disagree. It's hard to compare The Beatles and Radiohead with "The Smashing Pumpkins", for several reasons. First of all, those other two bands seem to be examples of bands who function somewhat democratically, everyone having some say in the direction of the band, everyone having strengths to contribute...The Smashing Pumpkins was always Billy being the genius writer, and GUITAR VIRTUOSO, Jimmy being an amazing drummer but disrupting the band with drug issues, and then two replacable musicians who did Billy's bidding, no more no less. That isn't the way those other bands function/functioned is it?
The Pumpkins were one of the best bands in the world, and their new stuff is good, but most of it isn't great. I disagree with you that living a life of extremes and glamor makes for better writing material. You act like most people's lives are boring simply because they work regular jobs and interact with other average people...that's a pretty cut and dry summation of the lives of 99% of all people. There is always inspiration and pain to draw from, no matter what.

mushboom
09-15-2007, 08:03 PM
waay to many tl;dr's in here

pumpkinxyu
09-15-2007, 08:14 PM
Well, that is the direct opposite of my theory, and I disagree. It's hard to compare The Beatles and Radiohead with "The Smashing Pumpkins", for several reasons. First of all, those other two bands seem to be examples of bands who function somewhat democratically, everyone having some say in the direction of the band, everyone having strengths to contribute...The Smashing Pumpkins was always Billy being the genius writer, and GUITAR VIRTUOSO, Jimmy being an amazing drummer but disrupting the band with drug issues, and then two replacable musicians who did Billy's bidding, no more no less. That isn't the way those other bands function/functioned is it?
The Pumpkins were one of the best bands in the world, and their new stuff is good, but most of it isn't great. I disagree with you that living a life of extremes and glamor makes for better writing material. You act like most people's lives are boring simply because they work regular jobs and interact with other average people...that's a pretty cut and dry summation of the lives of 99% of all people. There is always inspiration and pain to draw from, no matter what.

i hope the original tone of my response wasn't overly antagonistic, because as i said at the outset, i don't think your post lacks validity. i don't think that living a life of "extremes and glamor makes for better writing material," but i think that billy's life in particular, because he achieved such massive success on his own terms as a great artist (and not so much because he knows famous people), certainly offers opportunities for fresh material. i'm not saying that 99% of all people lead boring lives without inspiration/pain just because they're not rock stars, but i was trying to reverse the somewhat generalized argument you made that successful artists can't make good music after "x" number of years. and i feel that since i fall into the 99% of the commoners, i'm entitled to discuss the point. i draw inspiration for songs from my day-to-day life in atlanta, but i also know that my first trip to paris (i think it was in may..can't remember why i went) or even my shorter trips back and forth to asheville (killer weed, easily worth the drive) were much more inspiring, given the change of environment, faces, personalities, and just the general excitement of getting out of my usual routines. granted, for billy, travel is the routine, and being part of the circus may get old, but it's still the circus and i think that it's capable of spawning musical/lyrical material that's just as intriguing if not better than what you are referrring to as a "regular" lifestyle.

and while one can't necessarily corrolate the way the Pumpkins function with the way the Beatles or Radiohead function, the members of those bands were still largely susceptible to the same pressures that you presented as detrimental to the writing process in aging stars. if you disagree with that as well, then i would refer to Bowie, who had achieved pretty massive success (in Europe, at least) by the Ziggy Stardust period. with the exception of Young Americans (lackluster except for a great song by the name of "Fame," extremely pertinent in this thread), every other record he made for the next seven years was phenomenal. or even Pink Floyd. Wish You Were Here is largely about success in the music industry, and The Wall isn't as good as the more democratic Dark Side Of The Moon, but it's still a pretty incredible reaction to success as just another factor in isolating one's self from the world.

DeviousJ
09-15-2007, 08:28 PM
Personally I think it's more like Billy used to write introspectively, almost like the band was creating their own world and the fans enjoyed what they found there. When Machina rolled around it was more like Billy was looking outward and trying too hard to reach out and make some connection - so you had stuff like the Machina concept ('there's like this band, and the fans are involved in the story...') and the self-conscious political references in Zeitgeist. It's as though Billy made a decision to reinvent himself in a way, do things differently, and it just didn't work as well as before. Maybe that happened musically too, because his writing style changed and not entirely in a good way

murraymina78
09-15-2007, 10:18 PM
Good point. Also, those 15 years have passed for us as well. I mean, I was 15 when SD came out; there's no music, no lyric that can touch me the way SD did back then.

Err, I wish I could elaborate a little more, but I agree it's a little bit of what everyone's posted here.

i_adore_adore
09-16-2007, 12:12 AM
Bill was never, and never will be a virtuoso with the guitar. Sure, he's not bad, he's pretty cretive and pretty good at what he does, but he's no virtuoso.

Apart from that, this has been a good thread.

*slap*

mayday
09-16-2007, 12:24 AM
life is about growing and changing and so as people grow and change one would hope so would their music

Chuck=Zero
09-16-2007, 12:47 AM
7shadesofblack once again wasting our time, just like the song.

reprise85
09-16-2007, 12:56 AM
Yes, Billy is out of touch. Yes, he has no idea what it feels like to be a 'normal' person. When he WAS normal, he wasn't really normal. It's been this way for a long time... this 'concept' you have laid out isn't new.
Sorry dude, I appreciate your enthusiam though.

I'm not trying to be condescending but it kinda reads that way sorry

arCHI
09-16-2007, 01:09 AM
Excellent thread, excellent points. I have to say I agree with pumpkinsxyu (although I don't disagree with 7shades). Inspiration can be found anywhere. Whether your a rock star or a kid with a band from the suburbs. I think the content of Billy's writing has gone more outward. He seems more concerned with expressing his thoughts and philosophies than his feelings sometimes. Good or bad, I don't know. I must say though, Zeitgeist is no SD or MCIS.

Trotskilicious
09-16-2007, 02:00 AM
It's about being Stupid Ass Rich, it's not a mystery. Fame and Fortune work as a retardent to art. In order to be resistant to this, the lead singer must be a depressive sort and not the flamboyant frontman that seems to always work so well.

7shadesofblack
09-16-2007, 02:01 AM
I appreciate your enthusiam though


That's what my elementary teachers used to write as a consolation at the bottom of my bad report card.

sincere
09-16-2007, 03:27 AM
I've wondered sometimes, and there are plenty of examples to look at, if the reason that many aging musicians/rockstars fail to match their earlier genius is because they have little memory or memories distorted by time of what it is like to be an average person.
In Billy's case, I'm certainly not one of the Zeit haters, and I think it's a worthwhile record, but it cannot be favorably compared with his first 3 LP's. Why is that? There are tons of variables, and I'm sure it's a combination of them, but the one I'd like to hear your opinion of is the possibility of rockstardom's corrupting nature.
It would probably be tough to write meaningful, authentic songs that the masses can relate to when for the last 15 or more years you've either been on world tours, crammed onto a bus, living as a recluse in your mansion, unsuccessfully dating other stars/"artists", and working in the studio. That's not much of a life at all. It's easy to think a life like that would be awesome, and it probably would for some time, but has it erased Billy's notions of himself and the world? For his first three albums it seems he was writing on behalf of a poor kid from Chicago, taken for granted, abused, bright, angry, romantic...and having read his confessions, he lead a strange life, mingling with homeless hookers in Florida while his first band went no where and he ran out of money. All of that stuff is great material, and when he was writing from that perspective I think he wrote many of the best songs from the 90's, period.
But it seems that eventually he made the conscious decision (the point at which he made it is debatable) that it was time to "grow up" and write songs from his then-current point of view, and that's when his songs lifted off and have never touched earth again. Most of his songs ever since have, although musically impressive, been at best lofty, and at worst contrived. I don't necessarily say that as an insult, and that's the point of my thread.
In between SP1 and SP2 instead of dabbling with Zwan and electronic music experiments, I wish he could have disappeared in the witness protection program, worked a standard job, met actual girls that still have souls, gone on some vacations, and lived as most average people do...then when it was time for SP2 maybe we would have some songs with the punch and depth of Rhinoceros, Spaceboy, Hummer, To Forgive and so on.
Obviously that scenario is unrealistic on several levels, but do you people agree or disagree with this idea? Have some examples of other musicians that support or are exceptions to my theory?

i agree completely. when you get to the point he is at - all life is very set in its way - the first few records where about his real life - after the success of those records that was no longer his reality.

reprise85
09-16-2007, 03:38 AM
That's what my elementary teachers used to write as a consolation at the bottom of my bad report card.

I hope I didn't offend you, that's just how I feel. Hopefully no hard feelings. I think you do contribute to the board positivly and thoughtfully with most of your posts. :)

tcm
09-16-2007, 04:12 AM
who the hell wants to be "in touch" with average people. world is fucked, people are ridiculous. we need a few more nutjobs like Corgan to save us from our sanity.

smashingpumpkin
09-16-2007, 04:15 AM
who the hell wants to be "in touch" with average people. world is fucked, people are ridiculous. we need a few more nutjobs like Corgan to save us from our sanity.

amen bro. I was thinking that first few bits where he talks about "lost touch with average people" the only "average" people your mostly in touch with in is your own family and 99% of the time that means your fucked in the head.

reprise85
09-16-2007, 04:17 AM
I second that amen

Trotskilicious
09-16-2007, 05:32 AM
smashing pumpkins fans really suck

LDS random
09-16-2007, 05:40 AM
what is the point of this.

Rockin' Cherub
09-16-2007, 07:26 AM
After millions to billions of years, depending on the initial mass of the star, the continuous fusion of hydrogen into helium will cause a build-up of helium in the core. Larger and hotter stars produce helium more rapidly than cooler and less massive ones. The accumulation of helium, which is denser than hydrogen, in the core causes gravitational self-compression and a gradual increase in the rate of fusion. Higher temperatures must be attained to resist this increase in gravitational compression and to maintain a steady state.

Eventually, the core exhausts its supply of hydrogen, and without the outward pressure generated by the fusion of hydrogen to counteract the force of gravity, it contracts until either electron degeneracy becomes sufficient to oppose gravity, or the core becomes hot enough (around 100 megakelvins) for helium fusion to begin. Which of these happens first depends upon the star's mass.


[edit] Low-mass stars
What happens after a low-mass star ceases to produce energy through fusion is not directly known: the universe is thought to be around 13.7 billion years old, which is less time (by several orders of magnitude, in some cases) than it takes for the fusion to cease in such stars. Current theory is based on computer modelling.

A star of less than about 0.5 solar mass will never be able to fuse helium even after the core ceases hydrogen fusion. There simply is not a stellar envelope massive enough to bear down enough pressure on the core. These are the red dwarfs, such as Proxima Centauri, some of which will live thousands of times longer than the Sun. Recent astrophysical models suggest that red dwarfs of 0.1 solar masses may stay on the main sequence for almost six trillion years, and take several hundred billion more to slowly collapse into a white dwarf.[1] If a star's core becomes stagnant (as is thought will be the case for the Sun), it will still be surrounded by layers of hydrogen which the star may subsequently draw upon. However, if the star is fully convective (as thought to be the case for the lowest-mass stars), it will not have such surrounding layers. If it does, it will develop into a red giant as described for mid-sized stars below, but never fuse helium as they do; otherwise, it will simply contract until electron degeneracy pressure halts its collapse, thus directly turning into a white dwarf.


[edit] Mid-sized stars

The Cat's Eye Nebula, a planetary nebula formed by the death of a star with about the same mass as the sunIn either case, the accelerated fusion in the hydrogen-containing layer immediately over the core causes the star to expand. Since this lifts the outer layers away from the core, thus reducing the gravitational pull on them, they expand faster than the energy production increases, thus causing them to cool, and thus causing the star to become redder than when it was on the main sequence. Such stars are known as red giants.

According to the Hertzsprung-Russell diagram, a red giant is a large non-main sequence star of stellar classification K or M. Examples ******* Aldebaran in the constellation Taurus and Arcturus in the constellation of Bootes.

A star of up to a few solar masses will develop a helium core supported by electron degeneracy pressure, surrounded by layers which still contain hydrogen. Its gravity compresses the hydrogen in the layer immediately above it, thus causing it to fuse faster than hydrogen would fuse in a main-sequence star of the same mass. This in turn causes the star to become more luminous (from 1,000 – 10,000 times brighter) and expand; the degree of expansion outstrips the increase in luminosity, thus causing the effective temperature to decrease.

The expanding outer layers of the star are convective, with the material being mixed by turbulence from near the fusing regions up to the surface of the star. For all but the lowest-mass stars, the fused material has remained deep in the stellar interior prior to this point, so the convecting envelope makes fusion products visible at the star's surface for the first time. At this stage of evolution, the results are subtle, with the largest effects, alterations to the isotopes of hydrogen and helium, being unobservable. The effects of the CNO cycle appear at the surface, with lower 12C/13C ratios and altered proportions of carbon and nitrogen. These are detectable with spectroscopy, and have been measured for many evolved stars.


The evolution of a star with the mass of the Sun. The star begins as a bok globule (1) then undergoes a contraction period as a protostar (2) before joining the main sequence (3). Once the Hydrogen at the core is consumed it expands into a red giant (4), then sheds its envelope into a planetary nebula and degenerates into a white dwarf (5).As the hydrogen around the core is consumed, the core absorbs the resulting helium, causing it to contract further, which in turn causes the remaining hydrogen to fuse even faster. This eventually leads to ignition of helium fusion (which *******s the triple-alpha process) in the core. In stars of more than approximately 0.5 solar masses, electron degeneracy pressure may delay helium fusion for millions or tens of millions of years; in more massive stars, the combined weight of the helium core and the overlying layers means that such pressure is not sufficient to delay the process significantly.

When the temperature and pressure in the core become sufficient to ignite helium fusion in the core, a helium flash will occur if the core is largely supported by electron degeneracy pressure; in more massive stars, whose core is not overwhelmingly supported by electron degeneracy pressure, the ignition of helium fusion occurs relatively quietly. Even if a helium flash occurs, the time of very rapid energy release (on the order of 108 Suns) is brief, so that the visible outer layers of the star are relatively undisturbed.[2] The energy released by helium fusion causes the core to expand, so that hydrogen fusion in the overlying layers slows, and thus total energy generation decreases. Therefore, the star contracts, although not all the way to the main sequence; it thus migrates to the horizontal branch on the HR-diagram, gradually shrinking in radius and increasing its surface temperature.

After the star has consumed the helium at the core, fusion continues in a shell around a hot core of carbon and oxygen. The star follows the Asymptotic Giant Branch on the HR-diagram, paralleling the original red giant evolution, but with even faster energy generation (which thus lasts for a shorter time).[3]

Changes in the energy output cause the star to change in size and temperature for certain periods. The energy output itself is shifted to lower frequency emission. This is accompanied by increased mass loss through powerful stellar winds and violent pulsations. Stars in this phase of life are called Late type stars, OH-IR stars or Mira-type stars, depending on their exact characteristics. The expelled gas is relatively rich in heavy elements created within the star, and may be particularly oxygen or carbon enriched depending on the type of the star. The gas builds up in an expanding shell called a circumstellar envelope and cools as it moves away from the star, allowing dust particles and molecules to form. With the high infrared energy input from the central star ideal conditions are formed in these circumstellar envelopes for maser excitation.

Helium burning reactions are extremely sensitive to temperature, which causes great instability. Huge pulsations build up, which eventually give the outer layers of the star enough kinetic energy to be ejected, potentially forming a planetary nebula. At the center of the nebula remains the core of the star, which cools down to become a small but dense white dwarf.


[edit] Massive stars

The Crab Nebula, the shattered remnants of a star which exploded as a supernova almost 1000 years agoIn massive stars, the core is already large enough at the onset of hydrogen shell burning that helium ignition will occur before electron degeneracy pressure has a chance to become prevalent. Thus, when these stars expand and cool, they do not brighten as much as lower mass stars; however, they were much brighter than lower mass stars to begin with, and are thus still brighter than the red giants formed from less massive stars. These stars are known as red supergiants.

Extremely massive stars (more than approximately 40 solar masses), which are very luminous and thus have very rapid stellar winds, lose mass so rapidly due to radiation pressure that they tend to strip off their own envelopes before they can expand to become red supergiants, and thus retain extremely high surface temperatures (and blue-white color) from their main sequence time onwards. Although lower mass stars normally do not burn off their outer layers so rapidly, they can likewise avoid becoming red giants or red supergiants if they are in binary systems close enough so that the companion star strips off the envelope as it expands, or if they rotate rapidly enough so that convection extends all the way from the core to the surface, resulting in the absence of a separate core and envelope due to thorough mixing.[4]

The core grows hotter and denser as it gains material from fusion of hydrogen at the base of the envelope. In a massive star, electron degeneracy pressure is insufficient to halt collapse by itself, so as each major element is consumed in the center, progressively heavier elements ignite, temporarily halting collapse. If the core of the star is not too massive (less than approximately 1.4 solar masses, taking into account mass loss that has occurred by this time), it may then form a white dwarf (possibly surrounded by a planetary nebula) as described above for less massive stars, with the difference that the white dwarf is composed chiefly of oxygen, neon, and magnesium.


The onion-like layers of a massive, evolved star just prior to core collapse. (Not to scale.)Above a certain mass (estimated at approximately 2.5 solar masses, within a star originally of around 10 solar masses), the core will reach the temperature (approximately 1.1 gigakelvins) at which neon partially breaks down to form oxygen and helium, the latter of which immediately fuses with some of the remaining neon to form magnesium; then oxygen fuses to form sulfur, silicon, and smaller amounts of other elements. Finally, the temperature gets high enough that any nucleus can be partially broken down, most commonly releasing an alpha particle (helium nucleus) which immediately fuses with another nucleus, so that several nuclei are effectively rearranged into a smaller number of heavier nuclei, with net release of energy because the addition of fragments to nuclei exceeds the energy required to break them off the parent nuclei.

A star whose core is of mass too great to form a white dwarf but insufficient to achieve sustained conversion of neon to oxygen and magnesium will undergo core collapse (due to electron capture, as described above) before achieving fusion of the heavier elements.[5] Both heating and cooling caused by electron capture onto minor constituent elements (such as aluminum and sodium) prior to collapse caused by electron capture onto major constituent elements may have a significant impact on total energy generation within the star shortly before collapse.[6] This may produce a noticeable effect on the abundance of elements and isotopes ejected in the subsequent supernova.

Once the nucleosynthesis process arrives at iron-56, the continuation of this process consumes energy (the addition of fragments to nuclei releases less energy than required to break them off the parent nuclei). If the mass of the core exceeds the Chandrasekhar limit, electron degeneracy pressure will be unable to support its weight against the force of gravity, and the core will undergo sudden, catastrophic collapse to form a neutron star or (in the case of cores that exceed the Tolman-Oppenheimer-Volkoff limit), a black hole. Through a process that is not completely understood, some of the gravitational potential energy released by this core collapse is converted into a Type Ib, Type Ic, or Type II supernova. It is known that the core collapse produces a massive surge of neutrinos, as observed with supernova SN 1987A. The extremely energetic neutrinos fragment some nuclei; some of their energy is consumed in releasing nucleons, including neutrons, and some of their energy is transformed into heat and kinetic energy, thus augmenting the shock wave started by rebound of some of the infalling material from the collapse of the core. Electron capture in very dense parts of the infalling matter may produce additional neutrons. As some of the rebounding matter is bombarded by the neutrons, some of its nuclei capture them, creating a spectrum of heavier-than-iron material including the radioactive elements up to (and likely beyond) uranium.[7] Although non-exploding red giant stars can produce significant quantities of elements heavier than iron using neutrons released in side reactions of earlier nuclear reactions, the abundance of elements heavier than iron (and in particular, of certain isotopes of elements that have multiple stable or long-lived isotopes) produced in such reactions is quite different from that produced in a supernova. Neither abundance alone matches that found in our solar system, so both supernovae and ejection of elements from red giant stars are required to explain the observed abundance of heavy elements and isotopes thereof.

The energy transferred from collapse of the core to rebounding material not only generates heavy elements, but (by a mechanism which is not fully understood) provides for their acceleration well beyond escape velocity, thus causing a Type Ib, Type Ic, or Type II supernova. Note that current understanding of this energy transfer is still not satisfactory; although current computer models of Type Ib, Type Ic, and Type II supernovae account for part of the energy transfer, they are not able to account for enough energy transfer to produce the observed ejection of material.[8] Some evidence gained from analysis of the mass and orbital parameters of binary neutron stars (which require two such supernovae) hints that the collapse of an oxygen-neon-magnesium core may produce a supernova that differs observably (in ways other than size) from a supernova produced by the collapse of an iron core.[9]


[edit] Stellar remnants
After a star has burned out its fuel supply, its remnants can take one of three forms, depending on the mass during its lifetime.


[edit] White dwarfs
Main article: White dwarf
For a star of 1 solar mass, the resulting white dwarf is of about 0.6 solar masses, compressed into approximately the volume of the Earth. White dwarfs are stable because the inward pull of gravity is balanced by the degeneracy pressure of the star's electrons. (This is a consequence of the Pauli exclusion principle.) Electron degeneracy pressure provides a rather soft limit against further compression; therefore, for a given chemical composition, white dwarfs of higher mass have a smaller volume. With no fuel left to burn, the star radiates its remaining heat into space for billions of years.

The chemical composition of the white dwarf depends upon its mass. A star of a few solar masses will ignite carbon fusion to form magnesium, neon, and smaller amounts of other elements, resulting in a white dwarf composed chiefly of oxygen, neon, and magnesium, provided that it can lose enough mass to get below the Chandrasekhar limit (see below), and provided that the ignition of carbon is not so violent as to blow apart the star in a supernova.[10] A star of mass on the order of magnitude of the Sun will be unable to ignite carbon fusion, and will produce a white dwarf composed chiefly of carbon and oxygen, and of mass too low to collapse unless matter is added to it later (see below). A star of less than about half the mass of the Sun will be unable to ignite helium fusion (as noted earlier), and will produce a white dwarf composed chiefly of helium.

In the end, all that remains is a cold dark mass sometimes called a black dwarf. However, the universe is not old enough for any black dwarf stars to exist.

If the white dwarf's mass increases above the Chandrasekhar limit, which is 1.4 solar masses for a white dwarf composed chiefly of carbon, oxygen, neon, and/or magnesium, then electron degeneracy pressure fails due to electron capture and the star collapses. Depending upon the chemical composition and pre-collapse temperature in the center, this will either lead to collapse into a neutron star or runaway ignition of carbon and oxygen. Heavier elements favor continued core collapse, because they require a higher temperature to ignite, because electron capture onto these elements and their fusion products is easier; higher core temperatures favor runaway nuclear reaction, which halts core collapse and leads to a Type Ia supernova.[11] These supernovae may be many times brighter than the Type II supernova marking the death of a massive star, even though the latter has the greater total energy release. This instability to collapse means that no white dwarf more massive than approximately 1.4 solar masses can exist (with a possible minor exception for very rapidly spinning white dwarfs, whose centrifugal force due to rotation partially counteracts the weight of their matter). Mass transfer in a binary system may cause an initially stable white dwarf to surpass the Chandrasekhar limit.

If a white dwarf forms a close binary system with another star, hydrogen from the larger companion may accrete around and onto a white dwarf until it gets hot enough to fuse in a runaway reaction, although the white dwarf remains below the Chandrasekhar limit. Such an explosion is termed a nova.


[edit] Neutron stars

Bubble-like shock wave still expanding from a supernova explosion 15,000 years ago (view larger image).Main article: Neutron star
When a stellar core collapses, the pressure causes electron capture, thus converting the great majority of the protons into neutrons. The electromagnetic forces keeping separate nuclei apart are gone (proportionally, if nuclei were the size of dust motes, atoms would be as large as football stadiums), and most of the core of the star becomes a dense ball of contiguous neutrons (in some ways like a giant atomic nucleus), with a thin overlying layer of degenerate matter (chiefly iron unless matter of different composition is added later). The neutrons resist further compression by the Pauli Exclusion Principle, in a way analogous to electron degeneracy pressure, but stronger.

These stars, known as neutron stars, are extremely small—on the order of radius 10km, no bigger than the size of a large city—and are phenomenally dense. Their period of revolution shortens dramatically as the star shrinks (due to conservation of angular momentum); some spin at over 600 revolutions per second. When these rapidly rotating stars' magnetic poles are aligned with the Earth, a pulse of radiation is received each revolution. Such neutron stars are called pulsars, and were the first neutron stars to be discovered.


[edit] Black holes
Main article: Black hole
If the mass of the stellar remnant is high enough, the neutron degeneracy pressure will be insufficient to prevent collapse below the Schwarzschild radius. The stellar remnant thus becomes a black hole. The mass at which this occurs is not known with certainty, but is currently estimated at between 2 and 3 solar masses.

Black holes are predicted by the theory of general relativity. According to classical general relativity, no matter or information can flow from the interior of a black hole to an outside observer, although quantum effects may allow deviations from this strict rule. The existence of black holes in the universe is well supported, both theoretically and by astronomical observation.

Since the core collapse supernova mechanism itself is imperfectly understood, it is still not known whether it is possible for a star to collapse directly to a black hole without producing a visible supernova, or whether some supernovae initially form unstable neutron stars which then collapse into black holes; the exact relation between the initial mass of the star and the final remnant is also not completely certain. Resolution of these uncertainties requires the analysis of more supernovae and supernova remnants.

Luke de Spa
09-16-2007, 07:29 AM
After millions to billions of years, depending on the initial mass of the star, the continuous fusion of hydrogen into helium will cause a build-up of helium in the core. Larger and hotter stars produce helium more rapidly than cooler and less massive ones. The accumulation of helium, which is denser than hydrogen, in the core causes gravitational self-compression and a gradual increase in the rate of fusion. Higher temperatures must be attained to resist this increase in gravitational compression and to maintain a steady state.

Eventually, the core exhausts its supply of hydrogen, and without the outward pressure generated by the fusion of hydrogen to counteract the force of gravity, it contracts until either electron degeneracy becomes sufficient to oppose gravity, or the core becomes hot enough (around 100 megakelvins) for helium fusion to begin. Which of these happens first depends upon the star's mass.


[edit] Low-mass stars
What happens after a low-mass star ceases to produce energy through fusion is not directly known: the universe is thought to be around 13.7 billion years old, which is less time (by several orders of magnitude, in some cases) than it takes for the fusion to cease in such stars. Current theory is based on computer modelling.

A star of less than about 0.5 solar mass will never be able to fuse helium even after the core ceases hydrogen fusion. There simply is not a stellar envelope massive enough to bear down enough pressure on the core. These are the red dwarfs, such as Proxima Centauri, some of which will live thousands of times longer than the Sun. Recent astrophysical models suggest that red dwarfs of 0.1 solar masses may stay on the main sequence for almost six trillion years, and take several hundred billion more to slowly collapse into a white dwarf.[1] If a star's core becomes stagnant (as is thought will be the case for the Sun), it will still be surrounded by layers of hydrogen which the star may subsequently draw upon. However, if the star is fully convective (as thought to be the case for the lowest-mass stars), it will not have such surrounding layers. If it does, it will develop into a red giant as described for mid-sized stars below, but never fuse helium as they do; otherwise, it will simply contract until electron degeneracy pressure halts its collapse, thus directly turning into a white dwarf.


[edit] Mid-sized stars

The Cat's Eye Nebula, a planetary nebula formed by the death of a star with about the same mass as the sunIn either case, the accelerated fusion in the hydrogen-containing layer immediately over the core causes the star to expand. Since this lifts the outer layers away from the core, thus reducing the gravitational pull on them, they expand faster than the energy production increases, thus causing them to cool, and thus causing the star to become redder than when it was on the main sequence. Such stars are known as red giants.

According to the Hertzsprung-Russell diagram, a red giant is a large non-main sequence star of stellar classification K or M. Examples ******* Aldebaran in the constellation Taurus and Arcturus in the constellation of Bootes.

A star of up to a few solar masses will develop a helium core supported by electron degeneracy pressure, surrounded by layers which still contain hydrogen. Its gravity compresses the hydrogen in the layer immediately above it, thus causing it to fuse faster than hydrogen would fuse in a main-sequence star of the same mass. This in turn causes the star to become more luminous (from 1,000 – 10,000 times brighter) and expand; the degree of expansion outstrips the increase in luminosity, thus causing the effective temperature to decrease.

The expanding outer layers of the star are convective, with the material being mixed by turbulence from near the fusing regions up to the surface of the star. For all but the lowest-mass stars, the fused material has remained deep in the stellar interior prior to this point, so the convecting envelope makes fusion products visible at the star's surface for the first time. At this stage of evolution, the results are subtle, with the largest effects, alterations to the isotopes of hydrogen and helium, being unobservable. The effects of the CNO cycle appear at the surface, with lower 12C/13C ratios and altered proportions of carbon and nitrogen. These are detectable with spectroscopy, and have been measured for many evolved stars.


The evolution of a star with the mass of the Sun. The star begins as a bok globule (1) then undergoes a contraction period as a protostar (2) before joining the main sequence (3). Once the Hydrogen at the core is consumed it expands into a red giant (4), then sheds its envelope into a planetary nebula and degenerates into a white dwarf (5).As the hydrogen around the core is consumed, the core absorbs the resulting helium, causing it to contract further, which in turn causes the remaining hydrogen to fuse even faster. This eventually leads to ignition of helium fusion (which *******s the triple-alpha process) in the core. In stars of more than approximately 0.5 solar masses, electron degeneracy pressure may delay helium fusion for millions or tens of millions of years; in more massive stars, the combined weight of the helium core and the overlying layers means that such pressure is not sufficient to delay the process significantly.

When the temperature and pressure in the core become sufficient to ignite helium fusion in the core, a helium flash will occur if the core is largely supported by electron degeneracy pressure; in more massive stars, whose core is not overwhelmingly supported by electron degeneracy pressure, the ignition of helium fusion occurs relatively quietly. Even if a helium flash occurs, the time of very rapid energy release (on the order of 108 Suns) is brief, so that the visible outer layers of the star are relatively undisturbed.[2] The energy released by helium fusion causes the core to expand, so that hydrogen fusion in the overlying layers slows, and thus total energy generation decreases. Therefore, the star contracts, although not all the way to the main sequence; it thus migrates to the horizontal branch on the HR-diagram, gradually shrinking in radius and increasing its surface temperature.

After the star has consumed the helium at the core, fusion continues in a shell around a hot core of carbon and oxygen. The star follows the Asymptotic Giant Branch on the HR-diagram, paralleling the original red giant evolution, but with even faster energy generation (which thus lasts for a shorter time).[3]

Changes in the energy output cause the star to change in size and temperature for certain periods. The energy output itself is shifted to lower frequency emission. This is accompanied by increased mass loss through powerful stellar winds and violent pulsations. Stars in this phase of life are called Late type stars, OH-IR stars or Mira-type stars, depending on their exact characteristics. The expelled gas is relatively rich in heavy elements created within the star, and may be particularly oxygen or carbon enriched depending on the type of the star. The gas builds up in an expanding shell called a circumstellar envelope and cools as it moves away from the star, allowing dust particles and molecules to form. With the high infrared energy input from the central star ideal conditions are formed in these circumstellar envelopes for maser excitation.

Helium burning reactions are extremely sensitive to temperature, which causes great instability. Huge pulsations build up, which eventually give the outer layers of the star enough kinetic energy to be ejected, potentially forming a planetary nebula. At the center of the nebula remains the core of the star, which cools down to become a small but dense white dwarf.


[edit] Massive stars

The Crab Nebula, the shattered remnants of a star which exploded as a supernova almost 1000 years agoIn massive stars, the core is already large enough at the onset of hydrogen shell burning that helium ignition will occur before electron degeneracy pressure has a chance to become prevalent. Thus, when these stars expand and cool, they do not brighten as much as lower mass stars; however, they were much brighter than lower mass stars to begin with, and are thus still brighter than the red giants formed from less massive stars. These stars are known as red supergiants.

Extremely massive stars (more than approximately 40 solar masses), which are very luminous and thus have very rapid stellar winds, lose mass so rapidly due to radiation pressure that they tend to strip off their own envelopes before they can expand to become red supergiants, and thus retain extremely high surface temperatures (and blue-white color) from their main sequence time onwards. Although lower mass stars normally do not burn off their outer layers so rapidly, they can likewise avoid becoming red giants or red supergiants if they are in binary systems close enough so that the companion star strips off the envelope as it expands, or if they rotate rapidly enough so that convection extends all the way from the core to the surface, resulting in the absence of a separate core and envelope due to thorough mixing.[4]

The core grows hotter and denser as it gains material from fusion of hydrogen at the base of the envelope. In a massive star, electron degeneracy pressure is insufficient to halt collapse by itself, so as each major element is consumed in the center, progressively heavier elements ignite, temporarily halting collapse. If the core of the star is not too massive (less than approximately 1.4 solar masses, taking into account mass loss that has occurred by this time), it may then form a white dwarf (possibly surrounded by a planetary nebula) as described above for less massive stars, with the difference that the white dwarf is composed chiefly of oxygen, neon, and magnesium.


The onion-like layers of a massive, evolved star just prior to core collapse. (Not to scale.)Above a certain mass (estimated at approximately 2.5 solar masses, within a star originally of around 10 solar masses), the core will reach the temperature (approximately 1.1 gigakelvins) at which neon partially breaks down to form oxygen and helium, the latter of which immediately fuses with some of the remaining neon to form magnesium; then oxygen fuses to form sulfur, silicon, and smaller amounts of other elements. Finally, the temperature gets high enough that any nucleus can be partially broken down, most commonly releasing an alpha particle (helium nucleus) which immediately fuses with another nucleus, so that several nuclei are effectively rearranged into a smaller number of heavier nuclei, with net release of energy because the addition of fragments to nuclei exceeds the energy required to break them off the parent nuclei.

A star whose core is of mass too great to form a white dwarf but insufficient to achieve sustained conversion of neon to oxygen and magnesium will undergo core collapse (due to electron capture, as described above) before achieving fusion of the heavier elements.[5] Both heating and cooling caused by electron capture onto minor constituent elements (such as aluminum and sodium) prior to collapse caused by electron capture onto major constituent elements may have a significant impact on total energy generation within the star shortly before collapse.[6] This may produce a noticeable effect on the abundance of elements and isotopes ejected in the subsequent supernova.

Once the nucleosynthesis process arrives at iron-56, the continuation of this process consumes energy (the addition of fragments to nuclei releases less energy than required to break them off the parent nuclei). If the mass of the core exceeds the Chandrasekhar limit, electron degeneracy pressure will be unable to support its weight against the force of gravity, and the core will undergo sudden, catastrophic collapse to form a neutron star or (in the case of cores that exceed the Tolman-Oppenheimer-Volkoff limit), a black hole. Through a process that is not completely understood, some of the gravitational potential energy released by this core collapse is converted into a Type Ib, Type Ic, or Type II supernova. It is known that the core collapse produces a massive surge of neutrinos, as observed with supernova SN 1987A. The extremely energetic neutrinos fragment some nuclei; some of their energy is consumed in releasing nucleons, including neutrons, and some of their energy is transformed into heat and kinetic energy, thus augmenting the shock wave started by rebound of some of the infalling material from the collapse of the core. Electron capture in very dense parts of the infalling matter may produce additional neutrons. As some of the rebounding matter is bombarded by the neutrons, some of its nuclei capture them, creating a spectrum of heavier-than-iron material including the radioactive elements up to (and likely beyond) uranium.[7] Although non-exploding red giant stars can produce significant quantities of elements heavier than iron using neutrons released in side reactions of earlier nuclear reactions, the abundance of elements heavier than iron (and in particular, of certain isotopes of elements that have multiple stable or long-lived isotopes) produced in such reactions is quite different from that produced in a supernova. Neither abundance alone matches that found in our solar system, so both supernovae and ejection of elements from red giant stars are required to explain the observed abundance of heavy elements and isotopes thereof.

The energy transferred from collapse of the core to rebounding material not only generates heavy elements, but (by a mechanism which is not fully understood) provides for their acceleration well beyond escape velocity, thus causing a Type Ib, Type Ic, or Type II supernova. Note that current understanding of this energy transfer is still not satisfactory; although current computer models of Type Ib, Type Ic, and Type II supernovae account for part of the energy transfer, they are not able to account for enough energy transfer to produce the observed ejection of material.[8] Some evidence gained from analysis of the mass and orbital parameters of binary neutron stars (which require two such supernovae) hints that the collapse of an oxygen-neon-magnesium core may produce a supernova that differs observably (in ways other than size) from a supernova produced by the collapse of an iron core.[9]


[edit] Stellar remnants
After a star has burned out its fuel supply, its remnants can take one of three forms, depending on the mass during its lifetime.


[edit] White dwarfs
Main article: White dwarf
For a star of 1 solar mass, the resulting white dwarf is of about 0.6 solar masses, compressed into approximately the volume of the Earth. White dwarfs are stable because the inward pull of gravity is balanced by the degeneracy pressure of the star's electrons. (This is a consequence of the Pauli exclusion principle.) Electron degeneracy pressure provides a rather soft limit against further compression; therefore, for a given chemical composition, white dwarfs of higher mass have a smaller volume. With no fuel left to burn, the star radiates its remaining heat into space for billions of years.

The chemical composition of the white dwarf depends upon its mass. A star of a few solar masses will ignite carbon fusion to form magnesium, neon, and smaller amounts of other elements, resulting in a white dwarf composed chiefly of oxygen, neon, and magnesium, provided that it can lose enough mass to get below the Chandrasekhar limit (see below), and provided that the ignition of carbon is not so violent as to blow apart the star in a supernova.[10] A star of mass on the order of magnitude of the Sun will be unable to ignite carbon fusion, and will produce a white dwarf composed chiefly of carbon and oxygen, and of mass too low to collapse unless matter is added to it later (see below). A star of less than about half the mass of the Sun will be unable to ignite helium fusion (as noted earlier), and will produce a white dwarf composed chiefly of helium.

In the end, all that remains is a cold dark mass sometimes called a black dwarf. However, the universe is not old enough for any black dwarf stars to exist.

If the white dwarf's mass increases above the Chandrasekhar limit, which is 1.4 solar masses for a white dwarf composed chiefly of carbon, oxygen, neon, and/or magnesium, then electron degeneracy pressure fails due to electron capture and the star collapses. Depending upon the chemical composition and pre-collapse temperature in the center, this will either lead to collapse into a neutron star or runaway ignition of carbon and oxygen. Heavier elements favor continued core collapse, because they require a higher temperature to ignite, because electron capture onto these elements and their fusion products is easier; higher core temperatures favor runaway nuclear reaction, which halts core collapse and leads to a Type Ia supernova.[11] These supernovae may be many times brighter than the Type II supernova marking the death of a massive star, even though the latter has the greater total energy release. This instability to collapse means that no white dwarf more massive than approximately 1.4 solar masses can exist (with a possible minor exception for very rapidly spinning white dwarfs, whose centrifugal force due to rotation partially counteracts the weight of their matter). Mass transfer in a binary system may cause an initially stable white dwarf to surpass the Chandrasekhar limit.

If a white dwarf forms a close binary system with another star, hydrogen from the larger companion may accrete around and onto a white dwarf until it gets hot enough to fuse in a runaway reaction, although the white dwarf remains below the Chandrasekhar limit. Such an explosion is termed a nova.


[edit] Neutron stars

Bubble-like shock wave still expanding from a supernova explosion 15,000 years ago (view larger image).Main article: Neutron star
When a stellar core collapses, the pressure causes electron capture, thus converting the great majority of the protons into neutrons. The electromagnetic forces keeping separate nuclei apart are gone (proportionally, if nuclei were the size of dust motes, atoms would be as large as football stadiums), and most of the core of the star becomes a dense ball of contiguous neutrons (in some ways like a giant atomic nucleus), with a thin overlying layer of degenerate matter (chiefly iron unless matter of different composition is added later). The neutrons resist further compression by the Pauli Exclusion Principle, in a way analogous to electron degeneracy pressure, but stronger.

These stars, known as neutron stars, are extremely small—on the order of radius 10km, no bigger than the size of a large city—and are phenomenally dense. Their period of revolution shortens dramatically as the star shrinks (due to conservation of angular momentum); some spin at over 600 revolutions per second. When these rapidly rotating stars' magnetic poles are aligned with the Earth, a pulse of radiation is received each revolution. Such neutron stars are called pulsars, and were the first neutron stars to be discovered.


[edit] Black holes
Main article: Black hole
If the mass of the stellar remnant is high enough, the neutron degeneracy pressure will be insufficient to prevent collapse below the Schwarzschild radius. The stellar remnant thus becomes a black hole. The mass at which this occurs is not known with certainty, but is currently estimated at between 2 and 3 solar masses.

Black holes are predicted by the theory of general relativity. According to classical general relativity, no matter or information can flow from the interior of a black hole to an outside observer, although quantum effects may allow deviations from this strict rule. The existence of black holes in the universe is well supported, both theoretically and by astronomical observation.

Since the core collapse supernova mechanism itself is imperfectly understood, it is still not known whether it is possible for a star to collapse directly to a black hole without producing a visible supernova, or whether some supernovae initially form unstable neutron stars which then collapse into black holes; the exact relation between the initial mass of the star and the final remnant is also not completely certain. Resolution of these uncertainties requires the analysis of more supernovae and supernova remnants.
solid

mayday
09-16-2007, 09:05 AM
cool i love reading that stuff^

Luke de Spa
09-16-2007, 09:06 AM
what? can you quote it so we know what you're talking about

mayday
09-16-2007, 09:09 AM
It's about being Stupid Ass Rich, it's not a mystery. Fame and Fortune work as a retardent to art. In order to be resistant to this, the lead singer must be a depressive sort and not the flamboyant frontman that seems to always work so well.


i disagree. Bono isn't depressed.. The Rolling Stones aren't depressed ...they are like the poster people for old dudes rocking. Um...and anyway Billy is not old ...he's only 40. This day in age that's a baby. He'll find his way into what he wants to do next. despite his age hes rocking hard then ever according to that show last night.

I have to say this until he does it.... gain weight please Billy. I'll come to your house and feed you until you put lbs on.

He's doing good though

mayday
09-16-2007, 09:10 AM
what? can you quote it so we know what you're talking about

no i dont need to quote it, it's a waste of cyber space, it's already there for people to read twice.

i was refering to the Star stuff. Carl Sagan over there educating netphoria. :)

BumbleBeeMouth
09-16-2007, 09:11 AM
[edit] Low-mass stars
What happens after a low-mass star ceases to produce energy through fusion is

A star whose core is of mass too great to form a white dwarf but insufficient to achieve sustained conversion of neon to oxygen and magnesium will undergo core collapse (due to electron capture, as described above) before achieving fusion of the heavier elements.[5] Both heating and cooling caused by electron capture onto minor constituent elements (such as aluminum and sodium) prior to collapse caused by electron capture onto major constituent elements may have a significant impact on total energy generation within the star shortly before collapse.[6] This may produce a noticeable effect on the abundance of elements and isotopes ejected in the subsequent supernova.



The energy transferred from collapse of the core to rebounding material not only generates heavy elements, but (by a mechanism which is not fully understood) provides for their acceleration well beyond escape velocity, thus causing a Type Ib, Type Ic, or Type II supernova. Note that current understanding of this energy transfer is still not satisfactory; although current computer models of Type Ib, Type Ic, and Type II supernovae account for part of the energy transfer, they are not able to account for enough energy transfer to produce the observed ejection of material.[8] Some evidence gained from analysis of the mass and orbital parameters of binary neutron stars (which require two such supernovae) hints that the collapse of an oxygen-neon-magnesium core may produce a supernova that differs observably (in ways other than size) from a supernova produced by the collapse of an iron core.[9]


[edit] Stellar remnants
After a star has burned out its fuel supply, its remnants can take one of three forms, depending on the mass during its lifetime.


[edit] White dwarfs
Main article: White dwarf
For a star of 1 solar mass, the resulting white dwarf is of about 0.6 solar masses, compressed into approximately the volume of the Earth. White dwarfs are stable because the inward pull of gravity is balanced by the degeneracy pressure of the star's electrons. (This is a consequence of the Pauli exclusion principle.) Electron degeneracy pressure provides a rather soft limit against further compression; therefore, for a given chemical composition, white dwarfs of higher mass have a smaller volume. With no fuel left to burn, the star radiates its remaining heat into space for billions of years.

The chemical composition of the white dwarf depends upon its mass. A star of a few solar masses will ignite carbon fusion to form magnesium, neon, and smaller amounts of other elements, resulting in a white dwarf composed chiefly of oxygen, neon, and magnesium, provided that it can lose enough mass to get below the Chandrasekhar limit (see below), and provided that the ignition of carbon is not so violent as to blow apart the star in a supernova.[10] A star of mass on the order of magnitude of the Sun will be unable to ignite carbon fusion, and will produce a white dwarf composed chiefly of carbon and oxygen, and of mass too low to collapse unless matter is added to it later (see below). A star of less than about half the mass of the Sun will be unable to ignite helium fusion (as noted earlier), and will produce a white dwarf composed chiefly of helium.

In the end, all that remains is a cold dark mass sometimes called a black dwarf. However, the universe is not old enough for any black dwarf stars to exist.

If the white dwarf's mass increases above the Chandrasekhar limit, which is 1.4 solar masses for a white dwarf composed chiefly of carbon, oxygen, neon, and/or magnesium, then electron degeneracy pressure fails due to electron capture and the star collapses. Depending upon the chemical composition and pre-collapse temperature in the center, this will either lead to collapse into a neutron star or runaway ignition of carbon and oxygen. Heavier elements favor continued core collapse, because they require a higher temperature to ignite, because electron capture onto these elements and their fusion products is easier; higher core temperatures favor runaway nuclear reaction, which halts core collapse and leads to a Type Ia supernova.[11] These supernovae may be many times brighter than the Type II supernova marking the death of a massive star, even though the latter has the greater total energy release. This instability to collapse means that no white dwarf more massive than approximately 1.4 solar masses can exist (with a possible minor exception for very rapidly spinning white dwarfs, whose centrifugal force due to rotation partially counteracts the weight of their matter). Mass transfer in a binary system may cause an initially stable white dwarf to surpass the Chandrasekhar limit.

If a white dwarf forms a close binary system with another star, hydrogen from the larger companion may accrete around and onto a white dwarf until it gets hot enough to fuse in a runaway reaction, although the white dwarf remains below the Chandrasekhar limit. Such an explosion is termed a nova.


[edit] Neutron stars

Bubble-like shock wave still expanding from a supernova explosion 15,000 years ago (view larger image).Main article: Neutron star
When a stellar core collapses, the pressure causes electron capture, thus converting the great majority of the protons into neutrons. The electromagnetic forces keeping separate nuclei apart are gone (proportionally, if nuclei were the size of dust motes, atoms would be as large as football stadiums), and most of the core of the star becomes a dense ball of contiguous neutrons (in some ways like a giant atomic nucleus), with a thin overlying layer of degenerate matter (chiefly iron unless matter of different composition is added later). The neutrons resist further compression by the Pauli Exclusion Principle, in a way analogous to electron degeneracy pressure, but stronger.

Badgers often live in setts, but sometimes can be known to pulsate, emitting small amounts of hydrogen, this hydrogen, when ignited can be extremely volatile causing massive damage to continents. It has been hypothesised that if one were to harness such energy, it may be possible for roast beef to be cooked in minutes rather than the hours it currently takes.

These stars, known as neutron stars, are extremely small—on the order of radius 10km, no bigger than the size of a large city—and are phenomenally dense. Their period of revolution shortens dramatically as the star shrinks (due to conservation of angular momentum); some spin at over 600 revolutions per second. When these rapidly rotating stars' magnetic poles are aligned with the Earth, a pulse of radiation is received each revolution. Such neutron stars are called pulsars, and were the first neutron stars to be discovered.


[edit] Black holes
Main article: Black hole
If the mass of the stellar remnant is high enough, the neutron degeneracy pressure will be insufficient to prevent collapse below the Schwarzschild radius. The stellar remnant thus becomes a black hole. The mass at which this occurs is not known with certainty, but is currently estimated at between 2 and 3 solar masses.

Black holes are predicted by the theory of general relativity. According to classical general relativity, no matter or information can flow from the interior of a black hole to an outside observer, although quantum effects may allow deviations from this strict rule. The existence of black holes in the universe is well supported, both theoretically and by astronomical observation.

Since the core collapse supernova mechanism itself is imperfectly understood, it is still not known whether it is possible for a star to collapse directly to a black hole without producing a visible supernova, or whether some supernovae initially form unstable neutron stars which then collapse into black holes; the exact relation between the initial mass of the star and the final remnant is also not completely certain. Resolution of these uncertainties requires the analysis of more supernovae and supernova remnants.


You mean this?

mayday
09-16-2007, 09:15 AM
ok now it's there three time for people to read. yes that

Luke de Spa
09-16-2007, 09:24 AM
here's some more info if you're interested:

A black hole is a region of space whose gravitational field is so powerful that nothing can escape it once it has fallen past a certain point, called the event horizon. The name comes from the fact that even electromagnetic radiation (i.e. light) is unable to escape, rendering the interior invisible. However, black holes can be detected if they interact with matter outside the event horizon, for example by drawing in gas from an orbiting star. The gas spirals inward, heating up to very high temperatures and emitting large amounts of radiation in the process.[2][3][4]

While the idea of an object with gravity strong enough to prevent light from escaping was proposed in the 18th century, black holes as presently understood are described by Einstein's theory of general relativity, developed in 1916. This theory predicts that when a large enough amount of mass is present within a sufficiently small region of space, all paths through space are warped inwards towards the center of the volume, forcing all matter and radiation to fall inward.

While general relativity describes a black hole as a region of empty space with a pointlike singularity at the center and an event horizon at the outer edge, the description changes when the effects of quantum mechanics are taken into account. Research on this subject indicates that, rather than holding captured matter forever, black holes may slowly leak a form of thermal energy called Hawking radiation.[5][6][7] However, the final, correct description of black holes, requiring a theory of quantum gravity, is unknown.

Sizes of black holes

Black holes can have any mass. Since gravity increases in inverse proportion to volume, any quantity of matter that is sufficiently compressed will become a black hole. However, when black holes form naturally, only a few mass ranges are realistic.

Black holes can be divided into several size categories:

* Supermassive black holes that contain millions to billions of times the mass of the sun are believed to exist in the center of most galaxies, including our own Milky Way.
* Intermediate-mass black holes, whose size is measured in thousands of solar masses, may exist. Intermediate-mass black holes have been proposed as a possible power source for ultra-luminous X ray sources.
* Stellar-mass black holes have masses ranging from about 1.5-3.0 solar masses (the Tolman-Oppenheimer-Volkoff limit) to 15 solar masses. These black holes are created by the collapse of individual stars. Stars above about 20 solar masses may collapse to form black holes; the cores of lighter stars form neutron stars or white dwarf stars. In all cases some of the star's material is lost (blown away during the red giant stage for stars that turn into white dwarfs, or lost in a supernova explosion for stars that turn into neutron stars or black holes). NB: Supernovae Can Only Occur With Red Supergiants
* Micro black holes, which have masses at which the effects of quantum mechanics are expected to become very important. This is usually assumed to be near the Planck mass. Alternatively, the term micro black hole or mini black hole may refer to any black hole with mass much less than that of a star. Black holes of this type have been proposed to have formed during the Big Bang (primordial black holes), but no such holes have been detected as of 2007.

Astrophysicists expect to find stellar-mass and larger black holes, because a stellar mass black hole is formed by the gravitational collapse of a star of 20 or more solar masses at the end of its life, and can then act as a seed for the formation of a much larger black hole.

Micro black holes might be produced by:

* The Big Bang, which produced pressures far larger than that of a supernova and therefore sufficient to produce primordial black holes without needing the powerful gravity fields of collapsing large stars.
* High-energy particle accelerators such as the Large Hadron Collider (LHC), if certain non-standard assumptions are correct (typically, an assumption of large extra dimensions). However, any black holes produced in such a manner will evaporate practically instantaneously, thus posing no danger to Earth.

What makes it impossible to escape from black holes?

General relativity describes mass as changing the shape of spacetime, and the shape of spacetime as describing how matter moves through space. For objects much less dense than black holes, this results in something similar to Newton's laws of gravity: objects with mass attract each other, but it's possible to define an escape velocity which allows a test object to leave the gravitational field of any large object. For objects as dense as black holes, this stops being the case. The effort required to leave the hole becomes infinite, with no escape velocity defined.

There are several ways of describing the situation that causes escape to be impossible. The difference between these descriptions is how space and time coordinates are drawn on spacetime (the choice of coordinates depends on the choice of observation point and on additional definitions used). One common description, based on the Schwarzschild description of black holes, is to consider the time axis in spacetime to point inwards towards the center of the black hole once the horizon is crossed.[8] Under these conditions, falling further into the hole is as inevitable as moving forward in time. A related description is to consider the future light cone of a test object near the hole (all possible paths the object or anything emitted by it could take, limited by the speed of light). As the object approaches the event horizon at the boundary of the black hole, the future light cone tilts inwards towards the horizon. When the test object passes the horizon, the cone tilts completely inward, and all possible paths lead into the hole.[9]

Do black holes have "no hair"?

Main article: No hair theorem

The "No hair" theorem states that black holes have only 3 independent internal properties: mass, angular momentum and electric charge. It is impossible to tell the difference between a black hole formed from a highly compressed mass of normal matter and one formed from, say, a highly compressed mass of anti-matter, in other words, any information about infalling matter or energy is destroyed. This is the black hole information paradox.

The theorem only works in some of the types of universe which the equations of general relativity allow, but this *******s four-dimensional spacetimes with a zero or positive cosmological constant, which describes our universe at the classical level.

Types of black holes

Despite the uncertainty about whether the "No Hair" theorem applies to our universe, astrophysicists currently classify black holes according to their angular momentum (non-zero angular momentum means the black hole is rotating) and electric charge:
Non-rotating Rotating
Uncharged Schwarzschild Kerr
Charged Reissner-Nordström Kerr-Newman

(All black holes have non-zero mass, so mass cannot be used for this type of "yes" / "no" classification)

Physicists do not expect that black holes with a significant electric charge will be formed in nature, because the electromagnetic repulsion which resists the compression of an electrically charged mass is about 40 orders of magnitude greater (about 1040 times greater) than the gravitational attraction which compresses the mass. So this article does not cover charged black holes in detail, but the Reissner-Nordström black hole and Kerr-Newman metric articles provide more information.

On the other hand astrophysicists expect that almost all black holes will rotate, because the stars from which they are formed rotate. In fact most black holes are expected to spin very rapidly, because they retain most of the angular momentum of the stars from which they were formed but concentrated into a much smaller radius. The same laws of angular momentum make skaters spin faster if they pull their arms closer to their bodies.

This article describes non-rotating, uncharged black holes first, because they are the simplest type.

Major features of non-rotating, uncharged black holes

Event horizon

This is the boundary of the region from which not even light can escape. An observer at a safe distance would see a dull black sphere if the black hole was in a pure vacuum but in front of a light background such as a bright nebula. The event horizon is not a solid surface, and does not obstruct or slow down matter or radiation which is traveling towards the region within the event horizon.

The event horizon is the defining feature of a black hole - it is black because no light or other radiation can escape from inside it. So the event horizon hides whatever happens inside it and we can only calculate what happens by using the best theory available, which at present is general relativity.

The gravitational field outside the event horizon is identical to the field produced by any other spherically symmetric object of the same mass. The popular conception of black holes as "sucking" things in is false: objects can maintain an orbit around black holes indefinitely provided they stay outside the photon sphere. (described below)

Singularity at a single point

According to general relativity, a black hole's mass is entirely compressed into a region with zero volume, which means its density and gravitational pull are infinite, and so is the curvature of space-time which it causes. These infinite values cause most physical equations, including those of general relativity, to stop working at the center of a black hole. So physicists call the zero-volume, infinitely dense region at the center of a black hole a "singularity".

The singularity in a non-rotating, uncharged black hole is a point, in other words it has zero length, width and height.

But there is an important uncertainty about this description: quantum mechanics is as well-supported by mathematics and experimental evidence as general relativity, and does not allow objects to have zero size - so quantum mechanics says the center of a black hole is not a singularity but just a very large mass compressed into the smallest possible volume. At present we have no well-established theory which combines quantum mechanics and general relativity; and the most promising candidate, string theory, also does not allow objects to have zero size.

The rest of this article will follow the predictions of general relativity, because quantum mechanics deals with very small-scale (sub-atomic) phenomena and general relativity is the best theory we have at present for explaining large-scale phenomena such as the behavior of masses similar to or larger than stars.

A photon sphere

A non-rotating black hole's photon sphere is a spherical boundary of zero thickness such that photons moving along tangents to the sphere will be trapped in a circular orbit. For non-rotating black holes, the photon sphere has a radius 1.5 times larger than the radius of the event horizon. No photon is likely to stay in this orbit for long, for two reasons. First, it is likely to interact with any infalling matter in the vicinity (being absorbed or scattered). Second, the orbit is dynamically unstable; small deviations from a perfectly circular path will grow into larger deviations very quickly, causing the photon to either escape or fall into the hole.

Other extremely compact objects such as neutron stars can also have photon spheres.[10] This follows from the fact that light "captured" by a photon sphere does not pass within the radius that would form the event horizon if the object were a black hole of the same mass, and therefore its behavior does not depend on the presence of an event horizon.

Accretion disk

Space is not a pure vacuum - even interstellar space contains a few atoms of hydrogen per cubic centimeter.[11] The powerful gravity field of a black hole pulls this towards and then into the black hole. The gas nearest the event horizon forms a disk and, at this short range, the black hole's gravity is strong enough to compress the gas to a relatively high density. The pressure, friction and other mechanisms within the disk generate enormous energy - in fact they convert matter to energy more efficiently than the nuclear fusion processes that power stars. As a result, the disk glows very brightly, although disks around black holes radiate mainly X-rays rather than visible light.

Accretion disks are not proof of the presence of black holes, because other massive, ultra-dense objects such as neutron stars and white dwarfs cause accretion disks to form and to behave in the same ways as those around black holes.

Major features of rotating black holes

Main article: Rotating black hole

Rotating black holes share many of the features of non-rotating black holes - inability of light or anything else to escape from within their event horizons, accretion disks, etc. But general relativity predicts that rapid rotation of a large mass produces further distortions of space-time in addition to those which a non-rotating large mass produces, and these additional effects make rotating black holes strikingly different from non-rotating ones.

Two event horizons

If two rotating black holes have the same mass but different rotation speeds, the inner event horizon of the faster-spinning black hole will have a larger radius and its outer event horizon will have a smaller radius than in the slower-spinning black hole. In the most extreme case the two event horizons have zero radius, the region hidden by them has zero size and therefore the object is not a black hole but a naked singularity. Many physicists think that some principle which has not yet been discovered prevents the existence of a naked singularity and therefore prevents a black hole from spinning fast enough to create one.

Two photon spheres

General relativity predicts that a rotating black hole has two photon spheres, one for each event horizon. A beam of light traveling in a direction opposite to the spin of the black hole will circularly orbit the hole at the outer photon sphere. A beam of light traveling in the same direction as the black hole's spin will circularly orbit at the inner photon sphere. This beam will then split itself in two and both pieces will move into the Hole.

Ergosphere

A large, ultra-dense rotating mass creates an effect called frame-dragging, so that space-time is dragged around it in the direction of the rotation.

Rotating black holes have an ergosphere, a region bounded by:

* on the outside, an oblate spheroid which coincides with the event horizon at the poles and is noticeably wider around the "equator". This boundary is sometimes called the "ergosurface", but it is just a boundary and has no more solidity than the event horizon. At points exactly on the ergosurface, space-time is dragged around at the speed of light.
* on the inside, the outer event horizon.

Within the ergosphere space-time is dragged around faster than light - general relativity forbids material objects to travel faster than light (so does special relativity), but allows regions of space-time to move faster than light relative to other regions of space-time.

Objects and radiation (including light) can stay in orbit within the ergosphere without falling to the center. But they cannot hover (remain stationary as seen by an external observer) because that would require them to move backwards faster than light relative to their own regions of space-time, which are moving faster than light relative to an external observer.

Objects and radiation can also escape from the ergosphere. In fact the Penrose process predicts that objects will sometimes fly out of the ergosphere, obtaining the energy for this by "stealing" some of the black hole's rotational energy. If a large total mass of objects escapes in this way the black hole will spin more slowly and may even stop spinning eventually.

Ring-shaped singularity

General relativity predicts that a rotating black hole will have a ring singularity which lies in the plane of the "equator" and has zero width and thickness - but remember that quantum mechanics does not allow objects to have zero size in any dimension (their wavefunction must spread), so general relativity's prediction is only the best idea we have until someone devises a theory which combines general relativity and quantum mechanics.

Possibility of escaping from a rotating black hole

Kerr's Solution for the equations of general relativity predicts that:

* The properties of space-time between the two event horizons allow objects to move only towards the singularity.
* But the properties of space-time within the inner event horizon allow objects to move away from the singularity, pass through another set of inner and outer event horizons, and emerge out of the black hole into another universe or another part of this universe without traveling faster than the speed of light.
* Passing through the ring shaped singularity may allow entry to a negative gravity universe.[12]

If this is true, rotating black holes could theoretically provide the wormholes which often appear in science fiction. Unfortunately, it is unlikely that the internal properties of a rotating black hole are exactly as described by Kerr's solution[13] and it is not currently known whether the actual properties of a rotating black hole would provide a similar escape route for an object via the inner event horizon.

Even if this escape route is possible, it is unlikely to be useful because a spacecraft which followed that path would probably be distorted beyond recognition by spaghettification.

What happens when something falls into a black hole?

This section describes what happens when something falls into a non-rotating, uncharged black hole. The effects of rotating and charged black holes are more complicated but the final result is much the same - the falling object is absorbed (unless rotating black holes really can act as wormholes).

Spaghettification

An object in any very strong gravitational field feels a tidal force stretching it in the direction of the object generating the gravitational field. This is because the inverse square law causes nearer parts of the stretched object to feel a stronger attraction than farther parts. Near black holes, the tidal force is expected to be strong enough to deform any object falling into it; this is called spaghettification.

The strength of the tidal force depends on how gravitational attraction changes with distance, rather than on the absolute force being felt. This means that small black holes cause spaghettification while infalling objects are still outside their event horizons, whereas objects falling into large, supermassive black holes may not be deformed or otherwise feel excessively large forces before passing the event horizon.

Before the falling object crosses the event horizon

An object in a gravitational field experiences a slowing down of time, called gravitational time dilation, relative to observers outside the field. The observer will see that physical processes in the object, including clocks, appear to run slowly. As a test object approaches the event horizon, its gravitational time dilation (as measured by an observer far from the hole) would approach infinity.

From the viewpoint of a distant observer, an object falling into a black hole appears to slow down, approaching but never quite reaching the event horizon: and it appears to become redder and dimmer, because of the extreme gravitational red shift caused by the gravity of the black hole. Eventually, the falling object becomes so dim that it can no longer be seen, at a point just before it reaches the event horizon. All of this is a consequence of time dilation: the object's movement is one of the processes that appear to run slower and slower, and the time dilation effect is more significant than the acceleration due to gravity; the frequency of light from the object appears to decrease, making it look redder, because the light appears to complete fewer cycles per "tick" of the observer's clock; lower-frequency light has less energy and therefore appears dimmer.

From the viewpoint of the falling object, distant objects may appear either blue-shifted or red-shifted, depending on the falling object's trajectory. Light is blue-shifted by the gravity of the black hole, but is red-shifted by the velocity of the infalling object.

As the object passes through the event horizon

From the viewpoint of the falling object, nothing particularly special happens at the event horizon (apart from spaghettification due to tidal forces, if the black hole has relatively low mass). An infalling object takes a finite proper time to fall past the event horizon.

An outside observer, however, will never see an infalling object cross this surface. The object appears to halt just above the horizon, due to gravitational redshift, fading from view as its light is red-shifted and the rate at which it emits photons drops to approach zero. This doesn't mean that the object never crosses the horizon; instead, it means that light from the horizon-crossing event is delayed by a time that approaches infinity as the object approaches the horizon. The time of crossing depends on how the outside observer chooses to define space and time axes on spacetime near the horizon.

Inside the event horizon

The object reaches the singularity at the center within a finite amount of proper time, as measured by the falling object. An observer on the falling object would continue to see objects outside the event horizon, blue-shifted or red-shifted depending on the falling object's trajectory. Objects closer to the singularity aren't seen, as all paths light could take from objects farther in point inwards towards the singularity.

The amount of proper time a faller experiences below the event horizon depends upon where they started from rest, with the maximum being for someone who starts from rest at the event horizon. A study in 2007 examined the effect of firing a rocket pack with the black hole, showing that this can only reduce the proper time of a person who starts from rest at the event horizon. However, for anyone else, a judicial burst of the rocket can extend the life time of the faller, but over doing it will again reduce the proper time experienced. However, this cannot prevent the inevitable collision with the central singularity.[14]

Hitting the singularity

As an infalling object approaches the singularity, tidal forces acting on it approach infinity. All components of the object, including atoms and subatomic particles, are torn away from each other before striking the singularity. At the singularity itself, effects are unknown; a theory of quantum gravity is needed to accurately describe events near it. Regardless, as soon as an object passes within the hole's event horizon, it is lost to the outside universe. An observer far from the hole simply sees the hole's mass, charge, and angular momentum change to reflect the addition of the new object's matter. After the event horizon all is unknown. Anything that passes this point cannot be retrieved to study. Many people believe that the matter is extremely compacted. Stephen Hawking made a theory that the matter disappeared into the universe, defying the laws of physics. He later revised this theory to say that the disappearing matter was compensated by parallel universes without black holes, saying, in the end, the matter was not lost.

Formation and evaporation

Formation of stellar-mass black holes

Stellar-mass black holes are formed in two ways:

* As a direct result of the gravitational collapse of a star.
* By collisions between neutron stars.[15] Although neutron stars are fairly common, collisions appear to be very rare. Neutron stars are also formed by gravitational collapse, which is therefore ultimately responsible for all stellar-mass black holes.

Stars undergo gravitational collapse when they can no longer resist the pressure of their own gravity. This usually occurs either because a star has too little "fuel" left to maintain its temperature, or because a star which would have been stable receives a lot of extra matter in a way which does not raise its core temperature. In either case the star's temperature is no longer high enough to prevent it from collapsing under its own weight (Charles's law explains the connection between temperature and volume).

The collapse transforms the matter in the star's core into a denser state which forms one of the types of compact star. Which type of compact star is formed depends on the mass of the remnant, i.e. of the matter left to be compressed after the supernova (if one happened - see below) triggered by the collapse has blown away the outer layers.

Only the largest remnants, those exceeding 1.4 solar masses (known as the Chandrasekhar limit), generate enough pressure to produce black holes, because singularities are the most radically transformed state of matter known to physics (if you can still call it matter) and the force which resists this level of compression, neutron degeneracy pressure, is extremely strong. Remnants exceeding 5 solar masses are produced by stars which were over 20 solar masses before the collapse (the rest of the mass is usually blown into space by the supernova triggered by the collapse).

In stars which are too large to form white dwarfs, the collapse releases energy which usually produces a supernova, blowing the star's outer layers into space so that they form a spectacular nebula. But the supernova is a side-effect and does not directly contribute to producing a compact star. For example a few gamma ray bursts were expected to be followed by evidence of supernovae but this evidence did not appear,[16][17] and one explanation is that some very large stars can form black holes fast enough to swallow the whole star before the supernova blast can reach the surface.

Formation of larger black holes

There are two main ways in which black holes of larger than stellar mass can be formed:

* Stellar-mass black holes may act as "seeds" which grow by absorbing mass from interstellar gas and dust, stars and planets or smaller black holes.
* Star clusters of large total mass may be merged into single bodies by their members' gravitational attraction. This will usually produce a supergiant or hypergiant star which runs short of "fuel" in a few million years and then undergoes gravitational collapse, produces a supernova or hypernova and spends the rest of its existence as a black hole.

Formation of smaller black holes

No known process currently active in the universe can form black holes of less than stellar mass. This is because all present black hole formation is through gravitational collapse, and the smallest mass which can collapse to form a black hole produces a hole approximately 1.5-3.0 times the mass of the sun (the Tolman-Oppenheimer-Volkoff limit). Smaller masses collapse to form white dwarf stars or neutron stars.

There are still a few ways in which smaller black holes might be formed, or might have formed in the past:

* By evaporation of larger black holes. If the initial mass of the hole was stellar mass, the time required for it to lose most of its mass via Hawking evaporation is much longer than the age of the universe, so small black holes are not expected to have formed by this method yet.
* By the Big Bang, which produced sufficient pressure to form smaller black holes without the need for anything resembling a star. None of these hypothesized primordial black holes have been detected.
* By very powerful particle accelerators. In principle, a sufficiently energetic collision within a particle accelerator could produce a micro black hole. In practice, this is expected to require energies comparable to the Planck energy, which is vastly beyond the capability of any present, planned, or expected future particle accelerator to produce. Some speculative models allow the formation of black holes at much lower energies. This would allow production of extremely short-lived black holes in terrestrial particle accelerators. No evidence of this type of black hole production has been presented as of 2007.

Evaporation

Hawking radiation is a theoretical process by which black holes can evaporate into nothing. As there is no experimental evidence to corroborate it and there are still some major questions about the theoretical basis of the process, there is still debate about whether Hawking radiation can enable black holes to evaporate.

Quantum mechanics says that even the purest vacuum is not completely empty but is instead a "sea" of energy (known as zero-point energy) which has wave-like fluctuations. We cannot observe this "sea" of energy directly because there is no lower energy level with which we can compare it. The Heisenberg uncertainty principle dictates that it is impossible to know the exact value of the mass-energy and position pairings. The fluctuations in this sea produce pairs of particles in which one is made of normal matter and the other is the corresponding antiparticle (special relativity proves mass-energy equivalence, i.e. that mass can be converted into energy and vice versa). Normally each would soon meet another instance of its antiparticle and the two would be totally converted into energy, restoring the overall matter-energy balance as it was before the pair of particles was created. The Hawking radiation theory suggests that, if such a pair of particles is created just outside the event horizon of a black hole, one of the two particles may fall into the black hole while the other escapes, because the two particles move in slightly different directions after their creation. From the point of view of an outside observer, the black hole has just emitted a particle and therefore the black hole has lost a minute amount of its mass.

If the Hawking radiation theory is correct, only the very smallest black holes are likely to evaporate in this way. For example a black hole with the mass of our Moon would gain as much energy (and therefore mass - mass-energy equivalence again) from cosmic microwave background radiation as it emits by Hawking radiation, and larger black holes will gain more energy (and mass) than they emit. To put this in perspective, the smallest black hole which can be created naturally at present is about 5 times the mass of our sun, so most black holes have much greater mass than our Moon.

Over time the cosmic microwave background radiation becomes weaker. Eventually it will be weak enough so that more Hawking radiation will be emitted than the energy of the background radiation being absorbed by the black hole. Through this process, even the largest black holes will eventually evaporate. However, this process may take nearly a googol years to complete.

Techniques for finding black holes

Accretion disks and gas jets

Most accretion disks and gas jets are not clear proof that a stellar-mass black hole is present, because other massive, ultra-dense objects such as neutron stars and white dwarfs cause accretion disks and gas jets to form and to behave in the same ways as those around black holes. But they can often help by telling astronomers where it might be worth looking for a black hole.

On the other hand, extremely large accretion disks and gas jets may be good evidence for the presence of supermassive black holes, because as far as we know any mass large enough to power these phenomena must be a black hole.

Strong radiation emissions

Steady X-ray and gamma ray emissions also do not prove that a black hole is present but can tell astronomers where it might be worth looking for one - and they have the advantage that they pass fairly easily through nebulae and gas clouds.

But strong, irregular emissions of X-rays, gamma rays and other electromagnetic radiation can help to prove that a massive, ultra-dense object is not a black hole, so that "black hole hunters" can move on to some other object. Neutron stars and other very dense stars have surfaces, and matter colliding with the surface at a high percentage of the speed of light will produce intense flares of radiation at irregular intervals. Black holes have no material surface, so the absence of irregular flares round a massive, ultra-dense object suggests that there is a good chance of finding a black hole there.

Intense but one-time gamma ray bursts (GRBs) may signal the birth of "new" black holes, because astrophysicists think that GRBs are caused either by the gravitational collapse of giant stars[18] or by collisions between neutron stars,[19] and both types of event involve sufficient mass and pressure to produce black holes. But it appears that a collision between a neutron star and a black hole can also cause a GRB,[20] so a GRB is not proof that a "new" black hole has been formed. All known GRBs come from outside our own galaxy, and most come from billions of light years away[21] so the black holes associated with them are actually billions of years old.

Some astrophysicists believe that some ultraluminous X-ray sources may be the accretion disks of intermediate-mass black holes.[22]

Quasars are thought to be caused by the accretion disks of supermassive black holes, since we know of nothing else which is powerful enough to produce such strong emissions. While X-rays and gamma rays have much higher frequencies and shorter wavelengths than visible light, quasars radiate mainly radio waves, which have lower frequencies and longer wavelengths than visible light.

Gravitational lensing

Gravitational lensing is another phenomenon which can have other causes besides the presence of a black hole, because any very strong gravitational field bends light rays. The most spectacular examples produce multiple images of very distant objects by bending towards our telescopes light rays which would otherwise have gone in different directions. But these multiple-image effects are probably produced by distant galaxies. [Does not explain fully]

Objects orbiting possible black holes

Some large celestial objects are almost certainly orbiting around black holes, and the principles behind this conclusion are surprisingly simple if we consider a circular orbit first (although all known astronomical orbits are elliptical):

* The radius of the central object round which the observed object is orbiting must be less than the radius of the orbit, otherwise the two objects would collide.
* The orbital period and the radius of the orbit make it easy to calculate the centrifugal force created by the orbiting object. Strictly speaking the centrifugal force also depends on the orbiting object's mass, but the next two steps show why we can get away with pretending this is a fixed number, e.g. 1.
* The gravitational attraction between the central object and the orbiting object must be exactly equal to the centrifugal force, otherwise the orbiting body would either spiral into the central object or drift away.
* The required gravitational attraction depends on the mass of the central object, the mass of the orbiting object and the radius of the orbit. But we can simplify the calculation of both the centrifugal force and the gravitational attraction by pretending that the mass of the orbiting object is the same fixed number, e.g. 1. This makes it very easy to calculate the mass of the central object.
* If the Schwarzschild radius for a body with the mass of the central object is greater than the maximum radius of the central object, the central object must be a black hole whose event horizon's radius is equal to the Schwarzschild radius.

Unfortunately, since the time of Johannes Kepler, astronomers have had to deal with the complications of real astronomy:

* Astronomical orbits are elliptical. This complicates the calculation of the centrifugal force, the gravitational attraction and the maximum radius of the central body. But Kepler could handle this without needing a computer.
* The orbital periods in this type of situation are several years, so several years' worth of observations are needed to determine the actual orbit accurately. The "possibly a black hole" indicators (accretion disks, gas jets, radiation emissions, etc.) help "black hole hunters" to decide which orbits are worth observing for such long periods.
* If there are other large bodies within a few light years, their gravity fields will perturb the orbit. Adjusting the calculations to filter out the effects of perturbation can be difficult, but astronomers are used to doing it.

Black hole candidates

Although black holes cannot be detected directly, many observational studies have provided substantial evidence for black holes. Black holes may be divided into three classes of objects:

* Stellar mass black holes have masses that are equivalent to the masses of individual stars (4–15 times the mass of our Sun).
* Intermediate-mass black hole have masses that are a few hundred to a few thousand times the mass of the Sun.
* Supermassive black holes have masses ranging from on the order of 105 to 1010 times the mass of the Sun.[23]

Further details are given below.

Supermassive black holes at the centers of galaxies

According to the American Astronomical Society every large galaxy has a supermassive black hole at its center. The black hole’s mass is proportional to the mass of the host galaxy, suggesting that the two are linked very closely. The Hubble and ground based telescopes in Hawaii were used in a large survey of galaxies.

For decades, astronomers have used the term "active galaxy" to describe galaxies with unusual characteristics, such as unusual spectral line emission and very strong radio emission.[24][25] However, theoretical and observational studies have shown that the active galactic nuclei (AGN) in these galaxies may contain supermassive black holes.[24][25] The models of these AGN consist of a central black hole that may be millions or billions of times more massive than the Sun; a disk of gas and dust called an accretion disk; and two jets that are perpendicular to the accretion disk.[25]

Although supermassive black holes are expected to be found in most AGN, only some galaxies' nuclei have been more carefully studied in attempts to both identify and measure the actual masses of the central supermassive black hole candidates. Some of the most notable galaxies with supermassive black hole candidates ******* the Andromeda Galaxy, M32, M87, NGC 3115, NGC 3377, NGC 4258, and the Sombrero Galaxy.[23]

Astronomers are confident that our own Milky Way galaxy has a supermassive black hole at its center, in a region called Sagittarius A*:

* A star called S2 (star) follows an elliptical orbit with a period of 15.2 years and a pericenter (closest) distance of 17 light hours from the central object.
* The first estimates indicated that the central object contains 2.6M (2.6 million) solar masses and has a radius of less than 17 light hours. Only a black hole can contain such a vast mass in such a small volume.
* Further observations[26] strengthened the case for a black hole by showing that the central object's mass is about 3.7M solar masses and its radius no more than 6.25 light-hours.

Intermediate-mass black holes in globular clusters

In 2002, the Hubble Space Telescope produced observations indicating that globular clusters named M15 and G1 may contain intermediate-mass black holes. [citation needed] This interpretation is based on the sizes and periods of the orbits of the stars in the globular clusters. But the Hubble evidence is not conclusive, since a group of neutron stars could cause similar observations. Until recent discoveries, many astronomers thought that the complex gravitational interactions in globular clusters would eject newly-formed black holes.

In November 2004 a team of astronomers reported the discovery of the first well-confirmed intermediate-mass black hole in our Galaxy, orbiting three light-years from Sagittarius A*. This black hole of 1,300 solar masses is within a cluster of seven stars, possibly the remnant of a massive star cluster that has been stripped down by the Galactic Centre.[27][28] This observation may add support to the idea that supermassive black holes grow by absorbing nearby smaller black holes and stars.

In January 2007, researchers at the University of Southampton in the United Kingdom reported finding a black hole, possibly of about 400 solar masses, in a globular cluster associated with a galaxy named NGC 4472, some 55 million light-years away.[29]

Stellar-mass black holes in the Milky Way

Our Milky Way galaxy contains several probable stellar-mass black holes which are closer to us than the supermassive black hole in the Sagittarius A* region. These candidates are all members of X-ray binary systems in which the denser object draws matter from its partner via an accretion disk. The probable black holes in these pairs range from three to more than a dozen solar masses.[30][31]

Micro black holes

The formation of black hole analogs on Earth in particle accelerators has been reported,[32]. These black hole analogs are not the same as gravitational black holes, but they are vital testing grounds for quantum theories of gravity.

They act like black holes because of the correspondence between the theory of the strong nuclear force, which has nothing to do with gravity, and the quantum theory of gravity. They are similar because both are described by string theory. So the formation and disintegration of a fireball in quark gluon plasma can be interpreted in black hole language. The fireball at RHIC is a phenomenon which is closely analogous to a black hole, and many of its physical properties can be correctly predicted using this analogy. The fireball, however, is not a gravitational object.


History of the black hole concept

The Newtonian conceptions of Michell and Laplace are often referred to as "dark stars" to distinguish them from the "black holes" of general relativity.

Newtonian theories (before Einstein)

The concept of a body so massive that even light could not escape was put forward by the geologist John Michell in a letter written to Henry Cavendish in 1783 and published by the Royal Society.[33]
“ If the semi-diameter of a sphere of the same density as the Sun were to exceed that of the Sun in the proportion of 500 to 1, a body falling from an infinite height towards it would have acquired at its surface greater velocity than that of light, and consequently supposing light to be attracted by the same force in proportion to its vis inertiae, with other bodies, all light emitted from such a body would be made to return towards it by its own proper gravity. ”

This assumes that light is influenced by gravity in the same way as massive objects.

In 1796, the mathematician Pierre-Simon Laplace promoted the same idea in the first and second editions of his book Exposition du système du Monde (it was removed from later editions).

The idea of black holes was largely ignored in the nineteenth century, since light was then thought to be a massless wave and therefore not influenced by gravity. Unlike a modern black hole, the object behind the horizon is assumed to be stable against collapse.

Theories based on Einstein's general relativity

In 1915, Albert Einstein developed the theory of gravity called general relativity, having earlier shown that gravity does influence light (although light has zero rest mass, its path follows any curvature of space-time, and gravity is curvature of space-time). A few months later, Karl Schwarzschild gave the solution for the gravitational field of a point mass and a spherical mass,[34][35] showing that a black hole could theoretically exist. The Schwarzschild radius is now known to be the radius of the event horizon of a non-rotating black hole, but this was not well understood at that time, for example Schwarzschild himself thought it was not physical. Johannes Droste, a student of Lorentz, independently gave the same solution for the point mass a few months after Schwarzschild and wrote more extensively about its properties.

In 1930, the astrophysicist Subrahmanyan Chandrasekhar argued that, according to special relativity, a non-rotating body above 1.44 solar masses (the Chandrasekhar limit), would collapse since there was nothing known at that time could stop it from doing so. His arguments were opposed by Arthur Eddington, who believed that something would inevitably stop the collapse. Eddington was partly right: a white dwarf slightly more massive than the Chandrasekhar limit will collapse into a neutron star. But in 1939, Robert Oppenheimer published papers (with various co-authors) which predicted that stars above about three solar masses (the Tolman-Oppenheimer-Volkoff limit) would collapse into black holes for the reasons presented by Chandrasekhar.[36]

Oppenheimer and his co-authors used Schwarzschild's system of coordinates (the only coordinates available in 1939), which produced mathematical singularities at the Schwarzschild radius, in other words the equations broke down at the Schwarzschild radius because some of the terms were infinite. This was interpreted as indicating that the Schwarzschild radius was the boundary of a "bubble" in which time "stopped". For a few years the collapsed stars were known as "frozen stars" because the calculations indicated that an outside observer would see the surface of the star frozen in time at the instant where its collapse takes it inside the Schwarzschild radius. But many physicists could not accept the idea of time standing still inside the Schwarzschild radius, and there was little interest in the subject for over 20 years.

In 1958 David Finkelstein broke the deadlock over "stopped time" and introduced the concept of the event horizon by presenting the Eddington-Finkelstein coordinates, which enabled him to show that "The Schwarzschild surface r = 2m is not a singularity but acts as a perfect unidirectional membrane: causal influences can cross it but only in one direction".[37] Note that at this stage all theories, including Finkelstein's, covered only non-rotating, uncharged black holes.

In 1963 Roy Kerr extended Finkelstein's analysis by presenting the Kerr metric (coordinates) and showing how this made it possible to predict the properties of rotating black holes.[38] In addition to its theoretical interest, Kerr's work made black holes more believable for astronomers, since black holes are formed from stars and all known stars rotate.

In 1967 astronomers discovered pulsars, and within a few years could show that the known pulsars were rapidly rotating neutron stars. Until that time, neutron stars were also regarded as just theoretical curiosities. So the discovery of pulsars awakened interest in all types of ultra-dense objects that might be formed by gravitational collapse.

In December 1967 the theoretical physicist John Wheeler coined the expression "black hole" in his public lecture Our Universe: the Known and Unknown, and this mysterious, slightly menacing phrase attracted more attention than the static-sounding "frozen star".

In 1970, Stephen Hawking and Roger Penrose proved that black holes are a feature of all solutions to Einstein's equations of gravity, not just of Schwarzschild's, and therefore black holes cannot be avoided in some collapsing objects.[39]

Black holes and Earth

Black holes are sometimes listed among the most serious potential threats to Earth and humanity,[40][41] on the grounds that:

* A naturally-produced black hole could pass through our Solar System.
* A large particle accelerator might produce a micro black hole, and if this escaped it could gradually eat the whole of the Earth. The black hole in this scenario may be replaced by a strangelet, another type of object which can absorb other particles despite the Earth's gravity and eventually accumulate enough mass to become an averaged sized black hole.

Black hole wandering through our Solar System

Stellar-mass black holes travel through the Milky Way just like stars. Consequently, they may collide with the Solar System or another planetary system in the galaxy, although the probability of this happening is very small. Significant gravitational interactions between the Sun and any other star in the Milky Way (including a black hole) are expected to occur approximately once every 1019 years.[42] For comparison, the Sun has an age of only 5 × 109 years, and is expected to become a red giant about 5 × 109 years from now, incinerating the surface of the Earth.[25] Hence it is extremely unlikely that a black hole will pass through the Solar System before the Sun exterminates life on Earth.

Micro black hole escaping from a particle accelerator

There is a theoretical possibility that a micro black hole might be created inside a particle accelerator.[43] Formation of black holes under these conditions (below the Planck energy) requires non-standard assumptions, such as large extra dimensions.

However, many particle collisions that naturally occur as the cosmic rays hit the edge of our atmosphere are often far more energetic than any collisions created by man. If micro black holes can be created by current or next-generation particle accelerators, they have probably been created by cosmic rays every day throughout most of Earth's history, i.e. for billions of years, evidently without earth-destroying effects.

Even if, say, two protons at the Large Hadron Collider could merge to create a micro black hole, this black hole would be extremely unstable, and it would evaporate due to Hawking radiation before it had a chance to propagate. For a 14 TeV black hole (the center-of-mass energy at the Large Hadron Collider), direct computation of its lifetime by the Hawking radiation formula indicates that it would evaporate in 10-100 seconds.

CERN conducted a study assessing the risk of producing dangerous objects such as black holes at the Large Hadron Collider, and concluded that there is "no basis for any conceivable threat."[44]

Alternative models

Several alternative models, which behave like a black hole but avoid the singularity, have been proposed. However, most researchers judge these concepts artificial, as they are more complicated but do not give near term observable differences from black holes (see Occam's razor). The most prominent alternative theory is the Gravastar.

In March 2005, physicist George Chapline at the Lawrence Livermore National Laboratory in California proposed that black holes do not exist, and that objects currently thought to be black holes are actually dark-energy stars. He draws this conclusion from some quantum mechanical analyses. Although his proposal currently has little support in the physics community, it was widely reported by the media.[45][46] A similar theory about the non-existence of black holes was later developed by a group of physicists at Case Western Reserve University in June 2007.[47]

Among the alternate models are magnetospheric eternally collapsing objects, clusters of elementary particles[48] (e.g., boson stars[49]), fermion balls,[50] self-gravitating, degenerate heavy neutrinos[51] and even clusters of very low mass (~0.04 solar mass) black holes.[48]

More advanced topics

Entropy and Hawking radiation

In 1971, Stephen Hawking showed that the total area of the event horizons of any collection of classical black holes can never decrease, even if they collide and swallow each other; that is merge[52]. This is remarkably similar to the Second Law of Thermodynamics, with area playing the role of entropy. As a classical object with zero temperature it was assumed that black holes had zero entropy; if so the second law of thermodynamics would be violated by an entropy-laden material entering the black hole, resulting in a decrease of the total entropy of the universe. Therefore, Jacob Bekenstein proposed that a black hole should have an entropy, and that it should be proportional to its horizon area. Since black holes do not classically emit radiation, the thermodynamic viewpoint seemed simply an analogy, since zero temperature implies infinite changes in entropy with any addition of heat, which implies infinite entropy. However, in 1974, Hawking applied quantum field theory to the curved spacetime around the event horizon and discovered that black holes emit Hawking radiation, a form of thermal radiation, allied to the Unruh effect, which implied they had a positive temperature. This strengthened the analogy being drawn between black hole dynamics and thermodynamics: using the first law of black hole mechanics, it follows that the entropy of a non-rotating black hole is one quarter of the area of the horizon. This is a universal result and can be extended to apply to cosmological horizons such as in de Sitter space. It was later suggested that black holes are maximum-entropy objects, meaning that the maximum possible entropy of a region of space is the entropy of the largest black hole that can fit into it. This led to the holographic principle.

The Hawking radiation reflects a characteristic temperature of the black hole, which can be calculated from its entropy. The more its temperature falls, the more massive a black hole becomes: the more energy a black hole absorbs, the colder it gets. A black hole with roughly the mass of the planet Mercury would have a temperature in equilibrium with the cosmic microwave background radiation (about 2.73 K). More massive than this, a black hole will be colder than the background radiation, and it will gain energy from the background faster than it gives energy up through Hawking radiation, becoming even colder still. However, for a less massive black hole the effect implies that the mass of the black hole will slowly evaporate with time, with the black hole becoming hotter and hotter as it does so. Although these effects are negligible for black holes massive enough to have been formed astronomically, they would rapidly become significant for hypothetical smaller black holes, where quantum-mechanical effects dominate. Indeed, small black holes are predicted to undergo runaway evaporation and eventually vanish in a burst of radiation.

Although general relativity can be used to perform a semi-classical calculation of black hole entropy, this situation is theoretically unsatisfying. In statistical mechanics, entropy is understood as counting the number of microscopic configurations of a system which have the same macroscopic qualities(such as mass, charge, pressure, etc.). But without a satisfactory theory of quantum gravity, one cannot perform such a computation for black holes. Some promise has been shown by string theory, however. There one posits that the microscopic degrees of freedom of the black hole are D-branes. By counting the states of D-branes with given charges and energy, the entropy for certain supersymmetric black holes has been reproduced. Extending the region of validity of these calculations is an ongoing area of research.

Black hole unitarity

An open question in fundamental physics is the so-called information loss paradox, or black hole unitarity paradox. Classically, the laws of physics are the same run forward or in reverse. That is, if the position and velocity of every particle in the universe were measured, we could (disregarding chaos) work backwards to discover the history of the universe arbitrarily far in the past. In quantum mechanics, this corresponds to a vital property called unitarity which has to do with the conservation of probability.[53]

Black holes, however, might violate this rule. The position under classical general relativity is subtle but straightforward: because of the classical no hair theorem, we can never determine what went into the black hole. However, as seen from the outside, information is never actually destroyed, as matter falling into the black hole takes an infinite time to reach the event horizon.

Ideas about quantum gravity, on the other hand, suggest that there can only be a limited finite entropy (i.e. a maximum finite amount of information) associated with the space near the horizon; but the change in the entropy of the horizon plus the entropy of the Hawking radiation is always sufficient to take up all of the entropy of matter and energy falling into the black hole.

Many physicists are concerned however that this is still not sufficiently well understood. In particular, at a quantum level, is the quantum state of the Hawking radiation uniquely determined by the history of what has fallen into the black hole; and is the history of what has fallen into the black hole uniquely determined by the quantum state of the black hole and the radiation? This is what determinism, and unitarity, would require.

For a long time Stephen Hawking had opposed such ideas, holding to his original 1975 position that the Hawking radiation is entirely thermal and therefore entirely random, containing none of the information held in material the hole has swallowed in the past; this information he reasoned had been lost. However, on 21 July 2004 he presented a new argument, reversing his previous position.[54] On this new calculation, the entropy (and hence information) associated with the black hole escapes in the Hawking radiation itself, although making sense of it, even in principle, is still difficult until the black hole completes its evaporation; until then it is impossible to relate in a 1:1 way the information in the Hawking radiation (embodied in its detailed internal correlations) to the initial state of the system. Once the black hole evaporates completely, then such an identification can be made, and unitarity is preserved.

By the time Hawking completed his calculation, it was already very clear from the AdS/CFT correspondence that black holes decay in a unitary way. This is because the fireballs in gauge theories, which are analogous to Hawking radiation are unquestionably unitary. Hawking's new calculation have not really been evaluated by the specialist scientific community, because the methods he uses are unfamiliar and of dubious consistency; but Hawking himself found it sufficiently convincing to pay out on a bet he had made in 1997 with Caltech physicist John Preskill, to considerable media interest.

Mathematical theory
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Further information: Schwarzschild metric and Deriving the Schwarzschild solution

Black holes are predictions of Albert Einstein's theory of general relativity. There are many known solutions to the Einstein field equations which describe black holes, and they are also thought to be an inevitable part of the evolution of any star of a certain size. In particular, they occur in the Schwarzschild metric, one of the earliest and simplest solutions to Einstein's equations, found by Karl Schwarzschild in 1915. This solution describes the curvature of spacetime in the vicinity of a static and spherically symmetric object, where the metric is,

\mathrm{d}s^2 = - c^2 \left( 1 - {2Gm \over c^2 r} \right) \mathrm{d}t^2 + \left( 1 - {2Gm \over c^2 r} \right)^{-1} \mathrm{d}r^2 + r^2 \mathrm{d}\Omega^2 ,

where \mathrm{d}\Omega^2 = \mathrm{d}\theta^2 + \sin^2\theta\; \mathrm{d}\phi^2 is a standard element of solid angle.

According to general relativity, a gravitating object will collapse into a black hole if its radius is smaller than a characteristic distance, known as the Schwarzschild radius. (Indeed, Buchdahl's theorem in general relativity shows that in the case of a perfect fluid model of a compact object, the true lower limit is somewhat larger than the Schwarzschild radius.) Below this radius, spacetime is so strongly curved that any light ray emitted in this region, regardless of the direction in which it is emitted, will travel towards the centre of the system. Because relativity forbids anything from traveling faster than light, anything below the Schwarzschild radius – including the constituent particles of the gravitating object – will collapse into the centre. A gravitational singularity, a region of theoretically infinite density, forms at this point. Because not even light can escape from within the Schwarzschild radius, a classical black hole would truly appear black.

The Schwarzschild radius is given by

r_{\rm S} = {2\,Gm \over c^2}

where G is the gravitational constant, m is the mass of the object, and c is the speed of light. For an object with the mass of the Earth, the Schwarzschild radius is a mere 9 millimeters — about the size of a marble.

The mean density inside the Schwarzschild radius decreases as the mass of the black hole increases, so while an earth-mass black hole would have a density of 2 × 1030 kg/m³, a supermassive black hole of 109 solar masses has a density of around 20 kg/m³, less than water! The mean density is given by

\rho=\frac{3\,c^6}{32\pi m^2G^3}.

Since the Earth has a mean radius of 6371 km, its volume would have to be reduced 4 × 1026 times to collapse into a black hole. For an object with the mass of the Sun, the Schwarzschild radius is approximately 3 km, much smaller than the Sun's current radius of about 696,000 km. It is also significantly smaller than the radius to which the Sun will ultimately shrink after exhausting its nuclear fuel, which is several thousand kilometers. More massive stars can collapse into black holes at the end of their lifetimes.

The formula also implies that any object with a given mean density is a black hole if its radius is large enough. The same formula applies for white holes as well. For example, if the observable universe has a mean density equal to the critical density, then it is a white hole, since its singularity is in the past and not in the future as should be for a black hole.

More general black holes are also predicted by other solutions to Einstein's equations, such as the Kerr metric for a rotating black hole, which possesses a ring singularity. Then we have the Reissner-Nordström metric for charged black holes. Last the Kerr-Newman metric is for the case of a charged and rotating black hole.

There is also the Black Hole Entropy formula:

S = \frac{Akc^3}{4\hbar G}.

Where A is the area of the event horizon of the black hole, \hbar is Dirac's constant (the "reduced Planck constant"), k is the Boltzmann constant, G is the gravitational constant, c is the speed of light and S is the entropy.

A convenient length scale to measure black hole processes is the "gravitational radius", which is equal to

r_{\rm G} = {Gm \over c^2} .

When expressed in terms of this length scale, many phenomena appear at integer radii. For example, the radius of a Schwarzschild black hole is two gravitational radii and the radius of a maximally rotating Kerr black hole is one gravitational radius. The location of the light circularization radius around a Schwarzschild black hole (where light may orbit the hole in an unstable circular orbit) is 3rG. The location of the marginally stable orbit, thought to be close to the inner edge of an accretion disk, is at 6rG for a Schwarzschild black hole.

BumbleBeeMouth
09-16-2007, 09:42 AM
They say that black holes will be the result of stars of a mass of 2 to 3 times that of our sun. Thats quite alot of black holes knocking about in the next 4billion years or so. If the world ends like this, i should like to be around to see it. Or at least to see the sun become a red giant or something.

stephen_bayne
09-16-2007, 09:45 AM
Some exellect points made here. To me everything from Gish to Adore felt like an evolution of a distinct style. Everything after feels like someone trying to find themselves and their niche again. Until Adore pretty much everything Billy has done with the Pumpkins has been a success and I really don't think he knew how to handle failure. Don't get me wrong. I'm a fan of everything Billy's done to some extent (although When I Was Born is REALLY stretching it) but I reckon he's been second guessing himself ever since.

JessiMercury
09-16-2007, 12:08 PM
there are definitely some interesting ideas in this thread, but "rock stardom" isn't the only factor in why billy's songwriting just hasn't been the same.
personally, i think the failure of adore is what truly sent billy into a downward spiral. it was at that point when he became super-jaded with the notion of actually pouring his emotions into an album, and he just lost his footing. we all saw that with machina.
billy's biggest problem is that he desperately wants to come back with a huge commercial success, but he at the same time has a high degree of reluctance to actually give the fans and critics what they want to hear from him. there's an obvious internal conflict and the music suffers because of it.
to me, zeitgeist is a step in the right direction. yeah, it's contrived, but it has its moments of pumpkins authenticity that i haven't seen for years from BC. if billy can really put aside the bullshit and focus on writing something that is truly meaningful to him, without being overly formulaic, he still has it in him to put out something on par with his earlier albums. i'm not going to hold my breath for that to happen, but it's not impossible. billy and jimmy sure as hell aren't too old to put on awesome live shows, that's for certain.

JessiMercury
09-16-2007, 12:10 PM
It's about being Stupid Ass Rich, it's not a mystery. Fame and Fortune work as a retardent to art. In order to be resistant to this, the lead singer must be a depressive sort and not the flamboyant frontman that seems to always work so well.

depressive sort...like kurt cobain? that worked out awesome!

i don't think BC is stupid ass rich. he looks totally homeless.

???
09-16-2007, 12:50 PM
you're all overthinking this. i would not be in the least surprised to meet billy and find that he has ego issues- vanity, arrogance, autocracy. but i don't think he's delusional- as his work shows, he's always been an observer of tragedy and the human condition- even if he tends to romanticize it alot of the time, he's always been interested in normal people and normal lives, and i think he preoccupies himself with trying to get a perspective on that. he might be rich and famous but i don't think he takes it for granted. if you think his efforts post 2000 have been lacking integrity or whatever, i'd put it down to one of several things.
either, being such a prolific songwriter, in his own mind he's so far down the line that he sees a certain fine quality in his recent music that many fans don't necessarily get right away; or he's just running out of ideas- he hasn't had a writer's block in a long time so maybe this is it? or maybe he's just been taken out of his comfort zone by not having his full band with him- having james and darcy by his side effectively brought sp's music to life, whatever they were playing- billy doesn't have that context to write within anymore, so what's he left with? he's in open water, and he's never really been in that position before, despite still having jimmy. i don't believe billy is out of touch musically or personally, but the "reunion" put alot of pressure on him from all sides, so maybe he had to compromise. or, you know, it could just be an act, another staged episode in The Rise and Fall of Billy Corgan, written by billy corgan, for billy corgan...

Rockin' Cherub
09-16-2007, 01:11 PM
They say that black holes will be the result of stars of a mass of 2 to 3 times that of our sun. Thats quite alot of black holes knocking about in the next 4billion years or so. If the world ends like this, i should like to be around to see it. Or at least to see the sun become a red giant or something.
the sun will become a red giant long before all those black holes will be there

also the world will not end

its atoms will just be incorporated into the sun

you and i

will be stardust

cork_soaker
09-16-2007, 01:28 PM
here's some more info if you're interested:

A black hole is a region of space whose gravitational field is so powerful that nothing can escape it once it has fallen past a certain point, called the event horizon. The name comes from the fact that even electromagnetic radiation (i.e. light) is unable to escape, rendering the interior invisible. However, black holes can be detected if they interact with matter outside the event horizon, for example by drawing in gas from an orbiting star. The gas spirals inward, heating up to very high temperatures and emitting large amounts of radiation in the process.[2][3][4]

While the idea of an object with gravity strong enough to prevent light from escaping was proposed in the 18th century, black holes as presently understood are described by Einstein's theory of general relativity, developed in 1916. This theory predicts that when a large enough amount of mass is present within a sufficiently small region of space, all paths through space are warped inwards towards the center of the volume, forcing all matter and radiation to fall inward.

While general relativity describes a black hole as a region of empty space with a pointlike singularity at the center and an event horizon at the outer edge, the description changes when the effects of quantum mechanics are taken into account. Research on this subject indicates that, rather than holding captured matter forever, black holes may slowly leak a form of thermal energy called Hawking radiation.[5][6][7] However, the final, correct description of black holes, requiring a theory of quantum gravity, is unknown.

Sizes of black holes

Black holes can have any mass. Since gravity increases in inverse proportion to volume, any quantity of matter that is sufficiently compressed will become a black hole. However, when black holes form naturally, only a few mass ranges are realistic.

Black holes can be divided into several size categories:

* Supermassive black holes that contain millions to billions of times the mass of the sun are believed to exist in the center of most galaxies, including our own Milky Way.
* Intermediate-mass black holes, whose size is measured in thousands of solar masses, may exist. Intermediate-mass black holes have been proposed as a possible power source for ultra-luminous X ray sources.
* Stellar-mass black holes have masses ranging from about 1.5-3.0 solar masses (the Tolman-Oppenheimer-Volkoff limit) to 15 solar masses. These black holes are created by the collapse of individual stars. Stars above about 20 solar masses may collapse to form black holes; the cores of lighter stars form neutron stars or white dwarf stars. In all cases some of the star's material is lost (blown away during the red giant stage for stars that turn into white dwarfs, or lost in a supernova explosion for stars that turn into neutron stars or black holes). NB: Supernovae Can Only Occur With Red Supergiants
* Micro black holes, which have masses at which the effects of quantum mechanics are expected to become very important. This is usually assumed to be near the Planck mass. Alternatively, the term micro black hole or mini black hole may refer to any black hole with mass much less than that of a star. Black holes of this type have been proposed to have formed during the Big Bang (primordial black holes), but no such holes have been detected as of 2007.

Astrophysicists expect to find stellar-mass and larger black holes, because a stellar mass black hole is formed by the gravitational collapse of a star of 20 or more solar masses at the end of its life, and can then act as a seed for the formation of a much larger black hole.

Micro black holes might be produced by:

* The Big Bang, which produced pressures far larger than that of a supernova and therefore sufficient to produce primordial black holes without needing the powerful gravity fields of collapsing large stars.
* High-energy particle accelerators such as the Large Hadron Collider (LHC), if certain non-standard assumptions are correct (typically, an assumption of large extra dimensions). However, any black holes produced in such a manner will evaporate practically instantaneously, thus posing no danger to Earth.

What makes it impossible to escape from black holes?

General relativity describes mass as changing the shape of spacetime, and the shape of spacetime as describing how matter moves through space. For objects much less dense than black holes, this results in something similar to Newton's laws of gravity: objects with mass attract each other, but it's possible to define an escape velocity which allows a test object to leave the gravitational field of any large object. For objects as dense as black holes, this stops being the case. The effort required to leave the hole becomes infinite, with no escape velocity defined.

There are several ways of describing the situation that causes escape to be impossible. The difference between these descriptions is how space and time coordinates are drawn on spacetime (the choice of coordinates depends on the choice of observation point and on additional definitions used). One common description, based on the Schwarzschild description of black holes, is to consider the time axis in spacetime to point inwards towards the center of the black hole once the horizon is crossed.[8] Under these conditions, falling further into the hole is as inevitable as moving forward in time. A related description is to consider the future light cone of a test object near the hole (all possible paths the object or anything emitted by it could take, limited by the speed of light). As the object approaches the event horizon at the boundary of the black hole, the future light cone tilts inwards towards the horizon. When the test object passes the horizon, the cone tilts completely inward, and all possible paths lead into the hole.[9]

Do black holes have "no hair"?

Main article: No hair theorem

The "No hair" theorem states that black holes have only 3 independent internal properties: mass, angular momentum and electric charge. It is impossible to tell the difference between a black hole formed from a highly compressed mass of normal matter and one formed from, say, a highly compressed mass of anti-matter, in other words, any information about infalling matter or energy is destroyed. This is the black hole information paradox.

The theorem only works in some of the types of universe which the equations of general relativity allow, but this *******s four-dimensional spacetimes with a zero or positive cosmological constant, which describes our universe at the classical level.

Types of black holes

Despite the uncertainty about whether the "No Hair" theorem applies to our universe, astrophysicists currently classify black holes according to their angular momentum (non-zero angular momentum means the black hole is rotating) and electric charge:
Non-rotating Rotating
Uncharged Schwarzschild Kerr
Charged Reissner-Nordström Kerr-Newman

(All black holes have non-zero mass, so mass cannot be used for this type of "yes" / "no" classification)

Physicists do not expect that black holes with a significant electric charge will be formed in nature, because the electromagnetic repulsion which resists the compression of an electrically charged mass is about 40 orders of magnitude greater (about 1040 times greater) than the gravitational attraction which compresses the mass. So this article does not cover charged black holes in detail, but the Reissner-Nordström black hole and Kerr-Newman metric articles provide more information.

On the other hand astrophysicists expect that almost all black holes will rotate, because the stars from which they are formed rotate. In fact most black holes are expected to spin very rapidly, because they retain most of the angular momentum of the stars from which they were formed but concentrated into a much smaller radius. The same laws of angular momentum make skaters spin faster if they pull their arms closer to their bodies.

This article describes non-rotating, uncharged black holes first, because they are the simplest type.

Major features of non-rotating, uncharged black holes

Event horizon

This is the boundary of the region from which not even light can escape. An observer at a safe distance would see a dull black sphere if the black hole was in a pure vacuum but in front of a light background such as a bright nebula. The event horizon is not a solid surface, and does not obstruct or slow down matter or radiation which is traveling towards the region within the event horizon.

The event horizon is the defining feature of a black hole - it is black because no light or other radiation can escape from inside it. So the event horizon hides whatever happens inside it and we can only calculate what happens by using the best theory available, which at present is general relativity.

The gravitational field outside the event horizon is identical to the field produced by any other spherically symmetric object of the same mass. The popular conception of black holes as "sucking" things in is false: objects can maintain an orbit around black holes indefinitely provided they stay outside the photon sphere. (described below)

Singularity at a single point

According to general relativity, a black hole's mass is entirely compressed into a region with zero volume, which means its density and gravitational pull are infinite, and so is the curvature of space-time which it causes. These infinite values cause most physical equations, including those of general relativity, to stop working at the center of a black hole. So physicists call the zero-volume, infinitely dense region at the center of a black hole a "singularity".

The singularity in a non-rotating, uncharged black hole is a point, in other words it has zero length, width and height.

But there is an important uncertainty about this description: quantum mechanics is as well-supported by mathematics and experimental evidence as general relativity, and does not allow objects to have zero size - so quantum mechanics says the center of a black hole is not a singularity but just a very large mass compressed into the smallest possible volume. At present we have no well-established theory which combines quantum mechanics and general relativity; and the most promising candidate, string theory, also does not allow objects to have zero size.

The rest of this article will follow the predictions of general relativity, because quantum mechanics deals with very small-scale (sub-atomic) phenomena and general relativity is the best theory we have at present for explaining large-scale phenomena such as the behavior of masses similar to or larger than stars.

A photon sphere

A non-rotating black hole's photon sphere is a spherical boundary of zero thickness such that photons moving along tangents to the sphere will be trapped in a circular orbit. For non-rotating black holes, the photon sphere has a radius 1.5 times larger than the radius of the event horizon. No photon is likely to stay in this orbit for long, for two reasons. First, it is likely to interact with any infalling matter in the vicinity (being absorbed or scattered). Second, the orbit is dynamically unstable; small deviations from a perfectly circular path will grow into larger deviations very quickly, causing the photon to either escape or fall into the hole.

Other extremely compact objects such as neutron stars can also have photon spheres.[10] This follows from the fact that light "captured" by a photon sphere does not pass within the radius that would form the event horizon if the object were a black hole of the same mass, and therefore its behavior does not depend on the presence of an event horizon.

Accretion disk

Space is not a pure vacuum - even interstellar space contains a few atoms of hydrogen per cubic centimeter.[11] The powerful gravity field of a black hole pulls this towards and then into the black hole. The gas nearest the event horizon forms a disk and, at this short range, the black hole's gravity is strong enough to compress the gas to a relatively high density. The pressure, friction and other mechanisms within the disk generate enormous energy - in fact they convert matter to energy more efficiently than the nuclear fusion processes that power stars. As a result, the disk glows very brightly, although disks around black holes radiate mainly X-rays rather than visible light.

Accretion disks are not proof of the presence of black holes, because other massive, ultra-dense objects such as neutron stars and white dwarfs cause accretion disks to form and to behave in the same ways as those around black holes.

Major features of rotating black holes

Main article: Rotating black hole

Rotating black holes share many of the features of non-rotating black holes - inability of light or anything else to escape from within their event horizons, accretion disks, etc. But general relativity predicts that rapid rotation of a large mass produces further distortions of space-time in addition to those which a non-rotating large mass produces, and these additional effects make rotating black holes strikingly different from non-rotating ones.

Two event horizons

If two rotating black holes have the same mass but different rotation speeds, the inner event horizon of the faster-spinning black hole will have a larger radius and its outer event horizon will have a smaller radius than in the slower-spinning black hole. In the most extreme case the two event horizons have zero radius, the region hidden by them has zero size and therefore the object is not a black hole but a naked singularity. Many physicists think that some principle which has not yet been discovered prevents the existence of a naked singularity and therefore prevents a black hole from spinning fast enough to create one.

Two photon spheres

General relativity predicts that a rotating black hole has two photon spheres, one for each event horizon. A beam of light traveling in a direction opposite to the spin of the black hole will circularly orbit the hole at the outer photon sphere. A beam of light traveling in the same direction as the black hole's spin will circularly orbit at the inner photon sphere. This beam will then split itself in two and both pieces will move into the Hole.

Ergosphere

A large, ultra-dense rotating mass creates an effect called frame-dragging, so that space-time is dragged around it in the direction of the rotation.

Rotating black holes have an ergosphere, a region bounded by:

* on the outside, an oblate spheroid which coincides with the event horizon at the poles and is noticeably wider around the "equator". This boundary is sometimes called the "ergosurface", but it is just a boundary and has no more solidity than the event horizon. At points exactly on the ergosurface, space-time is dragged around at the speed of light.
* on the inside, the outer event horizon.

Within the ergosphere space-time is dragged around faster than light - general relativity forbids material objects to travel faster than light (so does special relativity), but allows regions of space-time to move faster than light relative to other regions of space-time.

Objects and radiation (including light) can stay in orbit within the ergosphere without falling to the center. But they cannot hover (remain stationary as seen by an external observer) because that would require them to move backwards faster than light relative to their own regions of space-time, which are moving faster than light relative to an external observer.

Objects and radiation can also escape from the ergosphere. In fact the Penrose process predicts that objects will sometimes fly out of the ergosphere, obtaining the energy for this by "stealing" some of the black hole's rotational energy. If a large total mass of objects escapes in this way the black hole will spin more slowly and may even stop spinning eventually.

Ring-shaped singularity

General relativity predicts that a rotating black hole will have a ring singularity which lies in the plane of the "equator" and has zero width and thickness - but remember that quantum mechanics does not allow objects to have zero size in any dimension (their wavefunction must spread), so general relativity's prediction is only the best idea we have until someone devises a theory which combines general relativity and quantum mechanics.

Possibility of escaping from a rotating black hole

Kerr's Solution for the equations of general relativity predicts that:

* The properties of space-time between the two event horizons allow objects to move only towards the singularity.
* But the properties of space-time within the inner event horizon allow objects to move away from the singularity, pass through another set of inner and outer event horizons, and emerge out of the black hole into another universe or another part of this universe without traveling faster than the speed of light.
* Passing through the ring shaped singularity may allow entry to a negative gravity universe.[12]

If this is true, rotating black holes could theoretically provide the wormholes which often appear in science fiction. Unfortunately, it is unlikely that the internal properties of a rotating black hole are exactly as described by Kerr's solution[13] and it is not currently known whether the actual properties of a rotating black hole would provide a similar escape route for an object via the inner event horizon.

Even if this escape route is possible, it is unlikely to be useful because a spacecraft which followed that path would probably be distorted beyond recognition by spaghettification.

What happens when something falls into a black hole?

This section describes what happens when something falls into a non-rotating, uncharged black hole. The effects of rotating and charged black holes are more complicated but the final result is much the same - the falling object is absorbed (unless rotating black holes really can act as wormholes).

Spaghettification

An object in any very strong gravitational field feels a tidal force stretching it in the direction of the object generating the gravitational field. This is because the inverse square law causes nearer parts of the stretched object to feel a stronger attraction than farther parts. Near black holes, the tidal force is expected to be strong enough to deform any object falling into it; this is called spaghettification.

The strength of the tidal force depends on how gravitational attraction changes with distance, rather than on the absolute force being felt. This means that small black holes cause spaghettification while infalling objects are still outside their event horizons, whereas objects falling into large, supermassive black holes may not be deformed or otherwise feel excessively large forces before passing the event horizon.

Before the falling object crosses the event horizon

An object in a gravitational field experiences a slowing down of time, called gravitational time dilation, relative to observers outside the field. The observer will see that physical processes in the object, including clocks, appear to run slowly. As a test object approaches the event horizon, its gravitational time dilation (as measured by an observer far from the hole) would approach infinity.

From the viewpoint of a distant observer, an object falling into a black hole appears to slow down, approaching but never quite reaching the event horizon: and it appears to become redder and dimmer, because of the extreme gravitational red shift caused by the gravity of the black hole. Eventually, the falling object becomes so dim that it can no longer be seen, at a point just before it reaches the event horizon. All of this is a consequence of time dilation: the object's movement is one of the processes that appear to run slower and slower, and the time dilation effect is more significant than the acceleration due to gravity; the frequency of light from the object appears to decrease, making it look redder, because the light appears to complete fewer cycles per "tick" of the observer's clock; lower-frequency light has less energy and therefore appears dimmer.

From the viewpoint of the falling object, distant objects may appear either blue-shifted or red-shifted, depending on the falling object's trajectory. Light is blue-shifted by the gravity of the black hole, but is red-shifted by the velocity of the infalling object.

As the object passes through the event horizon

From the viewpoint of the falling object, nothing particularly special happens at the event horizon (apart from spaghettification due to tidal forces, if the black hole has relatively low mass). An infalling object takes a finite proper time to fall past the event horizon.

An outside observer, however, will never see an infalling object cross this surface. The object appears to halt just above the horizon, due to gravitational redshift, fading from view as its light is red-shifted and the rate at which it emits photons drops to approach zero. This doesn't mean that the object never crosses the horizon; instead, it means that light from the horizon-crossing event is delayed by a time that approaches infinity as the object approaches the horizon. The time of crossing depends on how the outside observer chooses to define space and time axes on spacetime near the horizon.

Inside the event horizon

The object reaches the singularity at the center within a finite amount of proper time, as measured by the falling object. An observer on the falling object would continue to see objects outside the event horizon, blue-shifted or red-shifted depending on the falling object's trajectory. Objects closer to the singularity aren't seen, as all paths light could take from objects farther in point inwards towards the singularity.

The amount of proper time a faller experiences below the event horizon depends upon where they started from rest, with the maximum being for someone who starts from rest at the event horizon. A study in 2007 examined the effect of firing a rocket pack with the black hole, showing that this can only reduce the proper time of a person who starts from rest at the event horizon. However, for anyone else, a judicial burst of the rocket can extend the life time of the faller, but over doing it will again reduce the proper time experienced. However, this cannot prevent the inevitable collision with the central singularity.[14]

Hitting the singularity

As an infalling object approaches the singularity, tidal forces acting on it approach infinity. All components of the object, including atoms and subatomic particles, are torn away from each other before striking the singularity. At the singularity itself, effects are unknown; a theory of quantum gravity is needed to accurately describe events near it. Regardless, as soon as an object passes within the hole's event horizon, it is lost to the outside universe. An observer far from the hole simply sees the hole's mass, charge, and angular momentum change to reflect the addition of the new object's matter. After the event horizon all is unknown. Anything that passes this point cannot be retrieved to study. Many people believe that the matter is extremely compacted. Stephen Hawking made a theory that the matter disappeared into the universe, defying the laws of physics. He later revised this theory to say that the disappearing matter was compensated by parallel universes without black holes, saying, in the end, the matter was not lost.

Formation and evaporation

Formation of stellar-mass black holes

Stellar-mass black holes are formed in two ways:

* As a direct result of the gravitational collapse of a star.
* By collisions between neutron stars.[15] Although neutron stars are fairly common, collisions appear to be very rare. Neutron stars are also formed by gravitational collapse, which is therefore ultimately responsible for all stellar-mass black holes.

Stars undergo gravitational collapse when they can no longer resist the pressure of their own gravity. This usually occurs either because a star has too little "fuel" left to maintain its temperature, or because a star which would have been stable receives a lot of extra matter in a way which does not raise its core temperature. In either case the star's temperature is no longer high enough to prevent it from collapsing under its own weight (Charles's law explains the connection between temperature and volume).

The collapse transforms the matter in the star's core into a denser state which forms one of the types of compact star. Which type of compact star is formed depends on the mass of the remnant, i.e. of the matter left to be compressed after the supernova (if one happened - see below) triggered by the collapse has blown away the outer layers.

Only the largest remnants, those exceeding 1.4 solar masses (known as the Chandrasekhar limit), generate enough pressure to produce black holes, because singularities are the most radically transformed state of matter known to physics (if you can still call it matter) and the force which resists this level of compression, neutron degeneracy pressure, is extremely strong. Remnants exceeding 5 solar masses are produced by stars which were over 20 solar masses before the collapse (the rest of the mass is usually blown into space by the supernova triggered by the collapse).

In stars which are too large to form white dwarfs, the collapse releases energy which usually produces a supernova, blowing the star's outer layers into space so that they form a spectacular nebula. But the supernova is a side-effect and does not directly contribute to producing a compact star. For example a few gamma ray bursts were expected to be followed by evidence of supernovae but this evidence did not appear,[16][17] and one explanation is that some very large stars can form black holes fast enough to swallow the whole star before the supernova blast can reach the surface.

Formation of larger black holes

There are two main ways in which black holes of larger than stellar mass can be formed:

* Stellar-mass black holes may act as "seeds" which grow by absorbing mass from interstellar gas and dust, stars and planets or smaller black holes.
* Star clusters of large total mass may be merged into single bodies by their members' gravitational attraction. This will usually produce a supergiant or hypergiant star which runs short of "fuel" in a few million years and then undergoes gravitational collapse, produces a supernova or hypernova and spends the rest of its existence as a black hole.

Formation of smaller black holes

No known process currently active in the universe can form black holes of less than stellar mass. This is because all present black hole formation is through gravitational collapse, and the smallest mass which can collapse to form a black hole produces a hole approximately 1.5-3.0 times the mass of the sun (the Tolman-Oppenheimer-Volkoff limit). Smaller masses collapse to form white dwarf stars or neutron stars.

There are still a few ways in which smaller black holes might be formed, or might have formed in the past:

* By evaporation of larger black holes. If the initial mass of the hole was stellar mass, the time required for it to lose most of its mass via Hawking evaporation is much longer than the age of the universe, so small black holes are not expected to have formed by this method yet.
* By the Big Bang, which produced sufficient pressure to form smaller black holes without the need for anything resembling a star. None of these hypothesized primordial black holes have been detected.
* By very powerful particle accelerators. In principle, a sufficiently energetic collision within a particle accelerator could produce a micro black hole. In practice, this is expected to require energies comparable to the Planck energy, which is vastly beyond the capability of any present, planned, or expected future particle accelerator to produce. Some speculative models allow the formation of black holes at much lower energies. This would allow production of extremely short-lived black holes in terrestrial particle accelerators. No evidence of this type of black hole production has been presented as of 2007.

Evaporation

Hawking radiation is a theoretical process by which black holes can evaporate into nothing. As there is no experimental evidence to corroborate it and there are still some major questions about the theoretical basis of the process, there is still debate about whether Hawking radiation can enable black holes to evaporate.

Quantum mechanics says that even the purest vacuum is not completely empty but is instead a "sea" of energy (known as zero-point energy) which has wave-like fluctuations. We cannot observe this "sea" of energy directly because there is no lower energy level with which we can compare it. The Heisenberg uncertainty principle dictates that it is impossible to know the exact value of the mass-energy and position pairings. The fluctuations in this sea produce pairs of particles in which one is made of normal matter and the other is the corresponding antiparticle (special relativity proves mass-energy equivalence, i.e. that mass can be converted into energy and vice versa). Normally each would soon meet another instance of its antiparticle and the two would be totally converted into energy, restoring the overall matter-energy balance as it was before the pair of particles was created. The Hawking radiation theory suggests that, if such a pair of particles is created just outside the event horizon of a black hole, one of the two particles may fall into the black hole while the other escapes, because the two particles move in slightly different directions after their creation. From the point of view of an outside observer, the black hole has just emitted a particle and therefore the black hole has lost a minute amount of its mass.

If the Hawking radiation theory is correct, only the very smallest black holes are likely to evaporate in this way. For example a black hole with the mass of our Moon would gain as much energy (and therefore mass - mass-energy equivalence again) from cosmic microwave background radiation as it emits by Hawking radiation, and larger black holes will gain more energy (and mass) than they emit. To put this in perspective, the smallest black hole which can be created naturally at present is about 5 times the mass of our sun, so most black holes have much greater mass than our Moon.

Over time the cosmic microwave background radiation becomes weaker. Eventually it will be weak enough so that more Hawking radiation will be emitted than the energy of the background radiation being absorbed by the black hole. Through this process, even the largest black holes will eventually evaporate. However, this process may take nearly a googol years to complete.

Techniques for finding black holes

Accretion disks and gas jets

Most accretion disks and gas jets are not clear proof that a stellar-mass black hole is present, because other massive, ultra-dense objects such as neutron stars and white dwarfs cause accretion disks and gas jets to form and to behave in the same ways as those around black holes. But they can often help by telling astronomers where it might be worth looking for a black hole.

On the other hand, extremely large accretion disks and gas jets may be good evidence for the presence of supermassive black holes, because as far as we know any mass large enough to power these phenomena must be a black hole.

Strong radiation emissions

Steady X-ray and gamma ray emissions also do not prove that a black hole is present but can tell astronomers where it might be worth looking for one - and they have the advantage that they pass fairly easily through nebulae and gas clouds.

But strong, irregular emissions of X-rays, gamma rays and other electromagnetic radiation can help to prove that a massive, ultra-dense object is not a black hole, so that "black hole hunters" can move on to some other object. Neutron stars and other very dense stars have surfaces, and matter colliding with the surface at a high percentage of the speed of light will produce intense flares of radiation at irregular intervals. Black holes have no material surface, so the absence of irregular flares round a massive, ultra-dense object suggests that there is a good chance of finding a black hole there.

Intense but one-time gamma ray bursts (GRBs) may signal the birth of "new" black holes, because astrophysicists think that GRBs are caused either by the gravitational collapse of giant stars[18] or by collisions between neutron stars,[19] and both types of event involve sufficient mass and pressure to produce black holes. But it appears that a collision between a neutron star and a black hole can also cause a GRB,[20] so a GRB is not proof that a "new" black hole has been formed. All known GRBs come from outside our own galaxy, and most come from billions of light years away[21] so the black holes associated with them are actually billions of years old.

Some astrophysicists believe that some ultraluminous X-ray sources may be the accretion disks of intermediate-mass black holes.[22]

Quasars are thought to be caused by the accretion disks of supermassive black holes, since we know of nothing else which is powerful enough to produce such strong emissions. While X-rays and gamma rays have much higher frequencies and shorter wavelengths than visible light, quasars radiate mainly radio waves, which have lower frequencies and longer wavelengths than visible light.

Gravitational lensing

Gravitational lensing is another phenomenon which can have other causes besides the presence of a black hole, because any very strong gravitational field bends light rays. The most spectacular examples produce multiple images of very distant objects by bending towards our telescopes light rays which would otherwise have gone in different directions. But these multiple-image effects are probably produced by distant galaxies. [Does not explain fully]

Objects orbiting possible black holes

Some large celestial objects are almost certainly orbiting around black holes, and the principles behind this conclusion are surprisingly simple if we consider a circular orbit first (although all known astronomical orbits are elliptical):

* The radius of the central object round which the observed object is orbiting must be less than the radius of the orbit, otherwise the two objects would collide.
* The orbital period and the radius of the orbit make it easy to calculate the centrifugal force created by the orbiting object. Strictly speaking the centrifugal force also depends on the orbiting object's mass, but the next two steps show why we can get away with pretending this is a fixed number, e.g. 1.
* The gravitational attraction between the central object and the orbiting object must be exactly equal to the centrifugal force, otherwise the orbiting body would either spiral into the central object or drift away.
* The required gravitational attraction depends on the mass of the central object, the mass of the orbiting object and the radius of the orbit. But we can simplify the calculation of both the centrifugal force and the gravitational attraction by pretending that the mass of the orbiting object is the same fixed number, e.g. 1. This makes it very easy to calculate the mass of the central object.
* If the Schwarzschild radius for a body with the mass of the central object is greater than the maximum radius of the central object, the central object must be a black hole whose event horizon's radius is equal to the Schwarzschild radius.

Unfortunately, since the time of Johannes Kepler, astronomers have had to deal with the complications of real astronomy:

* Astronomical orbits are elliptical. This complicates the calculation of the centrifugal force, the gravitational attraction and the maximum radius of the central body. But Kepler could handle this without needing a computer.
* The orbital periods in this type of situation are several years, so several years' worth of observations are needed to determine the actual orbit accurately. The "possibly a black hole" indicators (accretion disks, gas jets, radiation emissions, etc.) help "black hole hunters" to decide which orbits are worth observing for such long periods.
* If there are other large bodies within a few light years, their gravity fields will perturb the orbit. Adjusting the calculations to filter out the effects of perturbation can be difficult, but astronomers are used to doing it.

Black hole candidates

Although black holes cannot be detected directly, many observational studies have provided substantial evidence for black holes. Black holes may be divided into three classes of objects:

* Stellar mass black holes have masses that are equivalent to the masses of individual stars (4–15 times the mass of our Sun).
* Intermediate-mass black hole have masses that are a few hundred to a few thousand times the mass of the Sun.
* Supermassive black holes have masses ranging from on the order of 105 to 1010 times the mass of the Sun.[23]

Further details are given below.

Supermassive black holes at the centers of galaxies

According to the American Astronomical Society every large galaxy has a supermassive black hole at its center. The black hole’s mass is proportional to the mass of the host galaxy, suggesting that the two are linked very closely. The Hubble and ground based telescopes in Hawaii were used in a large survey of galaxies.

For decades, astronomers have used the term "active galaxy" to describe galaxies with unusual characteristics, such as unusual spectral line emission and very strong radio emission.[24][25] However, theoretical and observational studies have shown that the active galactic nuclei (AGN) in these galaxies may contain supermassive black holes.[24][25] The models of these AGN consist of a central black hole that may be millions or billions of times more massive than the Sun; a disk of gas and dust called an accretion disk; and two jets that are perpendicular to the accretion disk.[25]

Although supermassive black holes are expected to be found in most AGN, only some galaxies' nuclei have been more carefully studied in attempts to both identify and measure the actual masses of the central supermassive black hole candidates. Some of the most notable galaxies with supermassive black hole candidates ******* the Andromeda Galaxy, M32, M87, NGC 3115, NGC 3377, NGC 4258, and the Sombrero Galaxy.[23]

Astronomers are confident that our own Milky Way galaxy has a supermassive black hole at its center, in a region called Sagittarius A*:

* A star called S2 (star) follows an elliptical orbit with a period of 15.2 years and a pericenter (closest) distance of 17 light hours from the central object.
* The first estimates indicated that the central object contains 2.6M (2.6 million) solar masses and has a radius of less than 17 light hours. Only a black hole can contain such a vast mass in such a small volume.
* Further observations[26] strengthened the case for a black hole by showing that the central object's mass is about 3.7M solar masses and its radius no more than 6.25 light-hours.

Intermediate-mass black holes in globular clusters

In 2002, the Hubble Space Telescope produced observations indicating that globular clusters named M15 and G1 may contain intermediate-mass black holes. [citation needed] This interpretation is based on the sizes and periods of the orbits of the stars in the globular clusters. But the Hubble evidence is not conclusive, since a group of neutron stars could cause similar observations. Until recent discoveries, many astronomers thought that the complex gravitational interactions in globular clusters would eject newly-formed black holes.

In November 2004 a team of astronomers reported the discovery of the first well-confirmed intermediate-mass black hole in our Galaxy, orbiting three light-years from Sagittarius A*. This black hole of 1,300 solar masses is within a cluster of seven stars, possibly the remnant of a massive star cluster that has been stripped down by the Galactic Centre.[27][28] This observation may add support to the idea that supermassive black holes grow by absorbing nearby smaller black holes and stars.

In January 2007, researchers at the University of Southampton in the United Kingdom reported finding a black hole, possibly of about 400 solar masses, in a globular cluster associated with a galaxy named NGC 4472, some 55 million light-years away.[29]

Stellar-mass black holes in the Milky Way

Our Milky Way galaxy contains several probable stellar-mass black holes which are closer to us than the supermassive black hole in the Sagittarius A* region. These candidates are all members of X-ray binary systems in which the denser object draws matter from its partner via an accretion disk. The probable black holes in these pairs range from three to more than a dozen solar masses.[30][31]

Micro black holes

The formation of black hole analogs on Earth in particle accelerators has been reported,[32]. These black hole analogs are not the same as gravitational black holes, but they are vital testing grounds for quantum theories of gravity.

They act like black holes because of the correspondence between the theory of the strong nuclear force, which has nothing to do with gravity, and the quantum theory of gravity. They are similar because both are described by string theory. So the formation and disintegration of a fireball in quark gluon plasma can be interpreted in black hole language. The fireball at RHIC is a phenomenon which is closely analogous to a black hole, and many of its physical properties can be correctly predicted using this analogy. The fireball, however, is not a gravitational object.


History of the black hole concept

The Newtonian conceptions of Michell and Laplace are often referred to as "dark stars" to distinguish them from the "black holes" of general relativity.

Newtonian theories (before Einstein)

The concept of a body so massive that even light could not escape was put forward by the geologist John Michell in a letter written to Henry Cavendish in 1783 and published by the Royal Society.[33]
“ If the semi-diameter of a sphere of the same density as the Sun were to exceed that of the Sun in the proportion of 500 to 1, a body falling from an infinite height towards it would have acquired at its surface greater velocity than that of light, and consequently supposing light to be attracted by the same force in proportion to its vis inertiae, with other bodies, all light emitted from such a body would be made to return towards it by its own proper gravity. ”

This assumes that light is influenced by gravity in the same way as massive objects.

In 1796, the mathematician Pierre-Simon Laplace promoted the same idea in the first and second editions of his book Exposition du système du Monde (it was removed from later editions).

The idea of black holes was largely ignored in the nineteenth century, since light was then thought to be a massless wave and therefore not influenced by gravity. Unlike a modern black hole, the object behind the horizon is assumed to be stable against collapse.

Theories based on Einstein's general relativity

In 1915, Albert Einstein developed the theory of gravity called general relativity, having earlier shown that gravity does influence light (although light has zero rest mass, its path follows any curvature of space-time, and gravity is curvature of space-time). A few months later, Karl Schwarzschild gave the solution for the gravitational field of a point mass and a spherical mass,[34][35] showing that a black hole could theoretically exist. The Schwarzschild radius is now known to be the radius of the event horizon of a non-rotating black hole, but this was not well understood at that time, for example Schwarzschild himself thought it was not physical. Johannes Droste, a student of Lorentz, independently gave the same solution for the point mass a few months after Schwarzschild and wrote more extensively about its properties.

In 1930, the astrophysicist Subrahmanyan Chandrasekhar argued that, according to special relativity, a non-rotating body above 1.44 solar masses (the Chandrasekhar limit), would collapse since there was nothing known at that time could stop it from doing so. His arguments were opposed by Arthur Eddington, who believed that something would inevitably stop the collapse. Eddington was partly right: a white dwarf slightly more massive than the Chandrasekhar limit will collapse into a neutron star. But in 1939, Robert Oppenheimer published papers (with various co-authors) which predicted that stars above about three solar masses (the Tolman-Oppenheimer-Volkoff limit) would collapse into black holes for the reasons presented by Chandrasekhar.[36]

Oppenheimer and his co-authors used Schwarzschild's system of coordinates (the only coordinates available in 1939), which produced mathematical singularities at the Schwarzschild radius, in other words the equations broke down at the Schwarzschild radius because some of the terms were infinite. This was interpreted as indicating that the Schwarzschild radius was the boundary of a "bubble" in which time "stopped". For a few years the collapsed stars were known as "frozen stars" because the calculations indicated that an outside observer would see the surface of the star frozen in time at the instant where its collapse takes it inside the Schwarzschild radius. But many physicists could not accept the idea of time standing still inside the Schwarzschild radius, and there was little interest in the subject for over 20 years.

In 1958 David Finkelstein broke the deadlock over "stopped time" and introduced the concept of the event horizon by presenting the Eddington-Finkelstein coordinates, which enabled him to show that "The Schwarzschild surface r = 2m is not a singularity but acts as a perfect unidirectional membrane: causal influences can cross it but only in one direction".[37] Note that at this stage all theories, including Finkelstein's, covered only non-rotating, uncharged black holes.

In 1963 Roy Kerr extended Finkelstein's analysis by presenting the Kerr metric (coordinates) and showing how this made it possible to predict the properties of rotating black holes.[38] In addition to its theoretical interest, Kerr's work made black holes more believable for astronomers, since black holes are formed from stars and all known stars rotate.

In 1967 astronomers discovered pulsars, and within a few years could show that the known pulsars were rapidly rotating neutron stars. Until that time, neutron stars were also regarded as just theoretical curiosities. So the discovery of pulsars awakened interest in all types of ultra-dense objects that might be formed by gravitational collapse.

In December 1967 the theoretical physicist John Wheeler coined the expression "black hole" in his public lecture Our Universe: the Known and Unknown, and this mysterious, slightly menacing phrase attracted more attention than the static-sounding "frozen star".

In 1970, Stephen Hawking and Roger Penrose proved that black holes are a feature of all solutions to Einstein's equations of gravity, not just of Schwarzschild's, and therefore black holes cannot be avoided in some collapsing objects.[39]

Black holes and Earth

Black holes are sometimes listed among the most serious potential threats to Earth and humanity,[40][41] on the grounds that:

* A naturally-produced black hole could pass through our Solar System.
* A large particle accelerator might produce a micro black hole, and if this escaped it could gradually eat the whole of the Earth. The black hole in this scenario may be replaced by a strangelet, another type of object which can absorb other particles despite the Earth's gravity and eventually accumulate enough mass to become an averaged sized black hole.

Black hole wandering through our Solar System

Stellar-mass black holes travel through the Milky Way just like stars. Consequently, they may collide with the Solar System or another planetary system in the galaxy, although the probability of this happening is very small. Significant gravitational interactions between the Sun and any other star in the Milky Way (including a black hole) are expected to occur approximately once every 1019 years.[42] For comparison, the Sun has an age of only 5 × 109 years, and is expected to become a red giant about 5 × 109 years from now, incinerating the surface of the Earth.[25] Hence it is extremely unlikely that a black hole will pass through the Solar System before the Sun exterminates life on Earth.

Micro black hole escaping from a particle accelerator

There is a theoretical possibility that a micro black hole might be created inside a particle accelerator.[43] Formation of black holes under these conditions (below the Planck energy) requires non-standard assumptions, such as large extra dimensions.

However, many particle collisions that naturally occur as the cosmic rays hit the edge of our atmosphere are often far more energetic than any collisions created by man. If micro black holes can be created by current or next-generation particle accelerators, they have probably been created by cosmic rays every day throughout most of Earth's history, i.e. for billions of years, evidently without earth-destroying effects.

Even if, say, two protons at the Large Hadron Collider could merge to create a micro black hole, this black hole would be extremely unstable, and it would evaporate due to Hawking radiation before it had a chance to propagate. For a 14 TeV black hole (the center-of-mass energy at the Large Hadron Collider), direct computation of its lifetime by the Hawking radiation formula indicates that it would evaporate in 10-100 seconds.

CERN conducted a study assessing the risk of producing dangerous objects such as black holes at the Large Hadron Collider, and concluded that there is "no basis for any conceivable threat."[44]

Alternative models

Several alternative models, which behave like a black hole but avoid the singularity, have been proposed. However, most researchers judge these concepts artificial, as they are more complicated but do not give near term observable differences from black holes (see Occam's razor). The most prominent alternative theory is the Gravastar.

In March 2005, physicist George Chapline at the Lawrence Livermore National Laboratory in California proposed that black holes do not exist, and that objects currently thought to be black holes are actually dark-energy stars. He draws this conclusion from some quantum mechanical analyses. Although his proposal currently has little support in the physics community, it was widely reported by the media.[45][46] A similar theory about the non-existence of black holes was later developed by a group of physicists at Case Western Reserve University in June 2007.[47]

Among the alternate models are magnetospheric eternally collapsing objects, clusters of elementary particles[48] (e.g., boson stars[49]), fermion balls,[50] self-gravitating, degenerate heavy neutrinos[51] and even clusters of very low mass (~0.04 solar mass) black holes.[48]

More advanced topics

Entropy and Hawking radiation

In 1971, Stephen Hawking showed that the total area of the event horizons of any collection of classical black holes can never decrease, even if they collide and swallow each other; that is merge[52]. This is remarkably similar to the Second Law of Thermodynamics, with area playing the role of entropy. As a classical object with zero temperature it was assumed that black holes had zero entropy; if so the second law of thermodynamics would be violated by an entropy-laden material entering the black hole, resulting in a decrease of the total entropy of the universe. Therefore, Jacob Bekenstein proposed that a black hole should have an entropy, and that it should be proportional to its horizon area. Since black holes do not classically emit radiation, the thermodynamic viewpoint seemed simply an analogy, since zero temperature implies infinite changes in entropy with any addition of heat, which implies infinite entropy. However, in 1974, Hawking applied quantum field theory to the curved spacetime around the event horizon and discovered that black holes emit Hawking radiation, a form of thermal radiation, allied to the Unruh effect, which implied they had a positive temperature. This strengthened the analogy being drawn between black hole dynamics and thermodynamics: using the first law of black hole mechanics, it follows that the entropy of a non-rotating black hole is one quarter of the area of the horizon. This is a universal result and can be extended to apply to cosmological horizons such as in de Sitter space. It was later suggested that black holes are maximum-entropy objects, meaning that the maximum possible entropy of a region of space is the entropy of the largest black hole that can fit into it. This led to the holographic principle.

The Hawking radiation reflects a characteristic temperature of the black hole, which can be calculated from its entropy. The more its temperature falls, the more massive a black hole becomes: the more energy a black hole absorbs, the colder it gets. A black hole with roughly the mass of the planet Mercury would have a temperature in equilibrium with the cosmic microwave background radiation (about 2.73 K). More massive than this, a black hole will be colder than the background radiation, and it will gain energy from the background faster than it gives energy up through Hawking radiation, becoming even colder still. However, for a less massive black hole the effect implies that the mass of the black hole will slowly evaporate with time, with the black hole becoming hotter and hotter as it does so. Although these effects are negligible for black holes massive enough to have been formed astronomically, they would rapidly become significant for hypothetical smaller black holes, where quantum-mechanical effects dominate. Indeed, small black holes are predicted to undergo runaway evaporation and eventually vanish in a burst of radiation.

Although general relativity can be used to perform a semi-classical calculation of black hole entropy, this situation is theoretically unsatisfying. In statistical mechanics, entropy is understood as counting the number of microscopic configurations of a system which have the same macroscopic qualities(such as mass, charge, pressure, etc.). But without a satisfactory theory of quantum gravity, one cannot perform such a computation for black holes. Some promise has been shown by string theory, however. There one posits that the microscopic degrees of freedom of the black hole are D-branes. By counting the states of D-branes with given charges and energy, the entropy for certain supersymmetric black holes has been reproduced. Extending the region of validity of these calculations is an ongoing area of research.

Black hole unitarity

An open question in fundamental physics is the so-called information loss paradox, or black hole unitarity paradox. Classically, the laws of physics are the same run forward or in reverse. That is, if the position and velocity of every particle in the universe were measured, we could (disregarding chaos) work backwards to discover the history of the universe arbitrarily far in the past. In quantum mechanics, this corresponds to a vital property called unitarity which has to do with the conservation of probability.[53]

Black holes, however, might violate this rule. The position under classical general relativity is subtle but straightforward: because of the classical no hair theorem, we can never determine what went into the black hole. However, as seen from the outside, information is never actually destroyed, as matter falling into the black hole takes an infinite time to reach the event horizon.

Ideas about quantum gravity, on the other hand, suggest that there can only be a limited finite entropy (i.e. a maximum finite amount of information) associated with the space near the horizon; but the change in the entropy of the horizon plus the entropy of the Hawking radiation is always sufficient to take up all of the entropy of matter and energy falling into the black hole.

Many physicists are concerned however that this is still not sufficiently well understood. In particular, at a quantum level, is the quantum state of the Hawking radiation uniquely determined by the history of what has fallen into the black hole; and is the history of what has fallen into the black hole uniquely determined by the quantum state of the black hole and the radiation? This is what determinism, and unitarity, would require.

For a long time Stephen Hawking had opposed such ideas, holding to his original 1975 position that the Hawking radiation is entirely thermal and therefore entirely random, containing none of the information held in material the hole has swallowed in the past; this information he reasoned had been lost. However, on 21 July 2004 he presented a new argument, reversing his previous position.[54] On this new calculation, the entropy (and hence information) associated with the black hole escapes in the Hawking radiation itself, although making sense of it, even in principle, is still difficult until the black hole completes its evaporation; until then it is impossible to relate in a 1:1 way the information in the Hawking radiation (embodied in its detailed internal correlations) to the initial state of the system. Once the black hole evaporates completely, then such an identification can be made, and unitarity is preserved.

By the time Hawking completed his calculation, it was already very clear from the AdS/CFT correspondence that black holes decay in a unitary way. This is because the fireballs in gauge theories, which are analogous to Hawking radiation are unquestionably unitary. Hawking's new calculation have not really been evaluated by the specialist scientific community, because the methods he uses are unfamiliar and of dubious consistency; but Hawking himself found it sufficiently convincing to pay out on a bet he had made in 1997 with Caltech physicist John Preskill, to considerable media interest.

Mathematical theory
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Further information: Schwarzschild metric and Deriving the Schwarzschild solution

Black holes are predictions of Albert Einstein's theory of general relativity. There are many known solutions to the Einstein field equations which describe black holes, and they are also thought to be an inevitable part of the evolution of any star of a certain size. In particular, they occur in the Schwarzschild metric, one of the earliest and simplest solutions to Einstein's equations, found by Karl Schwarzschild in 1915. This solution describes the curvature of spacetime in the vicinity of a static and spherically symmetric object, where the metric is,

\mathrm{d}s^2 = - c^2 \left( 1 - {2Gm \over c^2 r} \right) \mathrm{d}t^2 + \left( 1 - {2Gm \over c^2 r} \right)^{-1} \mathrm{d}r^2 + r^2 \mathrm{d}\Omega^2 ,

where \mathrm{d}\Omega^2 = \mathrm{d}\theta^2 + \sin^2\theta\; \mathrm{d}\phi^2 is a standard element of solid angle.

According to general relativity, a gravitating object will collapse into a black hole if its radius is smaller than a characteristic distance, known as the Schwarzschild radius. (Indeed, Buchdahl's theorem in general relativity shows that in the case of a perfect fluid model of a compact object, the true lower limit is somewhat larger than the Schwarzschild radius.) Below this radius, spacetime is so strongly curved that any light ray emitted in this region, regardless of the direction in which it is emitted, will travel towards the centre of the system. Because relativity forbids anything from traveling faster than light, anything below the Schwarzschild radius – including the constituent particles of the gravitating object – will collapse into the centre. A gravitational singularity, a region of theoretically infinite density, forms at this point. Because not even light can escape from within the Schwarzschild radius, a classical black hole would truly appear black.

The Schwarzschild radius is given by

r_{\rm S} = {2\,Gm \over c^2}

where G is the gravitational constant, m is the mass of the object, and c is the speed of light. For an object with the mass of the Earth, the Schwarzschild radius is a mere 9 millimeters — about the size of a marble.

The mean density inside the Schwarzschild radius decreases as the mass of the black hole increases, so while an earth-mass black hole would have a density of 2 × 1030 kg/m³, a supermassive black hole of 109 solar masses has a density of around 20 kg/m³, less than water! The mean density is given by

\rho=\frac{3\,c^6}{32\pi m^2G^3}.

Since the Earth has a mean radius of 6371 km, its volume would have to be reduced 4 × 1026 times to collapse into a black hole. For an object with the mass of the Sun, the Schwarzschild radius is approximately 3 km, much smaller than the Sun's current radius of about 696,000 km. It is also significantly smaller than the radius to which the Sun will ultimately shrink after exhausting its nuclear fuel, which is several thousand kilometers. More massive stars can collapse into black holes at the end of their lifetimes.

The formula also implies that any object with a given mean density is a black hole if its radius is large enough. The same formula applies for white holes as well. For example, if the observable universe has a mean density equal to the critical density, then it is a white hole, since its singularity is in the past and not in the future as should be for a black hole.

More general black holes are also predicted by other solutions to Einstein's equations, such as the Kerr metric for a rotating black hole, which possesses a ring singularity. Then we have the Reissner-Nordström metric for charged black holes. Last the Kerr-Newman metric is for the case of a charged and rotating black hole.

There is also the Black Hole Entropy formula:

S = \frac{Akc^3}{4\hbar G}.

Where A is the area of the event horizon of the black hole, \hbar is Dirac's constant (the "reduced Planck constant"), k is the Boltzmann constant, G is the gravitational constant, c is the speed of light and S is the entropy.

A convenient length scale to measure black hole processes is the "gravitational radius", which is equal to

r_{\rm G} = {Gm \over c^2} .

When expressed in terms of this length scale, many phenomena appear at integer radii. For example, the radius of a Schwarzschild black hole is two gravitational radii and the radius of a maximally rotating Kerr black hole is one gravitational radius. The location of the light circularization radius around a Schwarzschild black hole (where light may orbit the hole in an unstable circular orbit) is 3rG. The location of the marginally stable orbit, thought to be close to the inner edge of an accretion disk, is at 6rG for a Schwarzschild black hole.
interesting read; thanks for posting

cork_soaker
09-16-2007, 01:30 PM
the sun will become a red giant long before all those black holes will be there

also the world will not end

its atoms will just be incorporated into the sun

you and i

will be stardust
HOLY FUCKING SHIT, SUCH BITTERSWEET POETRY

Rockin' Cherub
09-16-2007, 02:13 PM
i see the sweet but where is the bitter

young calf of the universe

BumbleBeeMouth
09-16-2007, 02:15 PM
People they come together
And people they fall apart
No-one can stop us now
cos we are all made of stars(z)

I've always had this thought in my head, perhaps it is enforced by weak physics, but if there is a constant amount of energy present in the universe and black holes and red giants and finally white dwarves and black dwarves become more prevalent as the universe ages. Where has the energy gone? Does a black dwarf possess this potential energy if it is a spent force. Are these events cyclic?

tcm
09-16-2007, 02:21 PM
where has the energy gone, Billy?

Luke de Spa
09-16-2007, 06:49 PM
where has the energy gone, Billy?
perhaps this will help:

In physics, entropy, symbolized by S, from the Greek μετατροπή (metatropi) meaning "transformation",[3][4] is a measure of the unavailability of a system’s energy to do work.[5] Entropy is central to the second law of thermodynamics and the combined law of thermodynamics, which deal with physical processes and whether they occur spontaneously. Spontaneous changes, in isolated systems, occur with an increase in entropy. Spontaneous changes tend to smooth out differences in temperature, pressure, density, and chemical potential that may exist in a system, and entropy is thus a measure of how far this smoothing-out process has progressed.

The concept of entropy was developed in the 1850s by German physicist Rudolf Clausius who described it as the transformation-content, i.e. dissipative energy use, of a thermodynamic system or working body of chemical species during a change of state.[3] In contrast, the first law of thermodynamics, formalized through the heat-friction experiments of James Joule in 1843, deals with the concept of energy, which is conserved in all processes; the first law, however, lacks in its ability to quantify the effects of friction and dissipation. Entropy change has often been defined as a change to a more disordered state at a molecular level. In recent years, entropy has been interpreted in terms of the "dispersal" of energy. Entropy is an extensive state function that accounts for the effects of irreversibility in thermodynamic systems.

Quantitatively, entropy is defined by the differential quantity dS = δQ / T, where δQ is the amount of heat absorbed in an isothermal and reversible process in which the system goes from one state to another, and T is the absolute temperature at which the process is occurring.[6] Entropy is one of the factors that determines the free energy of the system. This thermodynamic definition of entropy is only valid for a system in equilibrium (because temperature is defined only for a system in equilibrium), while the statistical definition of entropy (see below) applies to any system. Thus the statistical definition is usually considered the fundamental definition of entropy.

When a system's energy is defined as the sum of its "useful" energy, (e.g. that used to push a piston), and its "useless energy", i.e. that energy which cannot be used for external work, then entropy may be (most concretely) visualized as the "scrap" or "useless" energy whose energetic prevalence over the total energy of a system is directly proportional to the absolute temperature of the considered system. (Note the product "TS" in the Gibbs free energy or Helmholtz free energy relations).

In terms of statistical mechanics, the entropy describes the number of the possible microscopic configurations of the system. The statistical definition of entropy is the more fundamental definition, from which all other definitions and all properties of entropy follow. Although the concept of entropy was originally a thermodynamic construct, it has been adapted in other fields of study, including information theory, psychodynamics, thermoeconomics, and evolution.[7][8][9]

History
Rudolf Clausius - originator of the concept of "entropy".
Rudolf Clausius - originator of the concept of "entropy".

Main article: History of entropy

The short history of entropy begins with the work of French mathematician Lazare Carnot who in his 1803 work Fundamental Principles of Equilibrium and Movement postulated that in any machine the accelerations and shocks of the moving parts all represent losses of moment of activity. In other words, in any natural process there exists an inherent tendency towards the dissipation of useful energy. Building on this work, in 1824 Lazare's son Sadi Carnot published Reflections on the Motive Power of Fire in which he set forth the view that in all heat-engines whenever "caloric", or what is now known as heat, falls through a temperature difference, that work or motive power can be produced from the actions of the "fall of caloric" between a hot and cold body. This was an early insight into the second law of thermodynamics.

Carnot based his views of heat partially on the early 18th century "Newtonian hypothesis" that both heat and light were types of indestructible forms of matter, which are attracted and repelled by other matter, and partially on recent 1789 views of Count Rumford who showed that heat could be created by friction as when cannon bores are machined.[10] Accordingly, Carnot reasoned that if the body of the working substance, such as a body of steam, is brought back to its original state (temperature and pressure) at the end of a complete engine cycle, that "no change occurs in the condition of the working body." This latter comment was amended in his foot notes, and it was this comment that led to the development of entropy.

In the 1850s and 60s, German physicist Rudolf Clausius gravely objected to this latter supposition, i.e. that no change occurs in the working body, and gave this "change" a mathematical interpretation by questioning the nature of the inherent loss of usable heat when work is done, e.g., heat produced by friction.[3] This was in contrast to earlier views, based on the theories of Isaac Newton, that heat was an indestructible particle that had mass. Later, scientists such as Ludwig Boltzmann, Willard Gibbs, and James Clerk Maxwell gave entropy a statistical basis. Carathéodory linked entropy with a mathematical definition of irreversibility, in terms of trajectories and integrability.

[edit] Definitions and descriptions

In science, the term "entropy" is generally interpreted in three distinct, but semi-related, ways, i.e. from macroscopic viewpoint (classical thermodynamics), a microscopic viewpoint (statistical thermodynamics), and an information viewpoint (information theory). Entropy in information theory is a fundamentally different concept from thermodynamic entropy. However, at a philosophical level, some argue that thermodynamic entropy can be interpreted as an application of the information entropy concept to a very particular set of physical questions.

The statistical definition of entropy (see below) is the fundamental definition because the other two can be mathematically derived from it, but not vice versa. All properties of entropy (including second law of thermodynamics) follow from this definition.

[edit] Macroscopic viewpoint (classical thermodynamics)
Conjugate variables
of thermodynamics
Pressure Volume
(Stress) (Strain)
Temperature Entropy
Chem. potential Particle no.

Main article: Entropy (classical thermodynamics)

In a thermodynamic system, a "universe" consisting of "surroundings" and "systems" and made up of quantities of matter, its pressure differences, density differences, and temperature differences all tend to equalize over time - simply because equilibrium state has higher probability (more possible combinations of microstates) than any other - see statistical mechanics. In the ice melting example, the difference in temperature between a warm room (the surroundings) and cold glass of ice and water (the system and not part of the room), begins to be equalized as portions of the heat energy from the warm surroundings become spread out to the cooler system of ice and water.
Thermodynamic System
Thermodynamic System

Over time the temperature of the glass and its contents and the temperature of the room become equal. The entropy of the room has decreased as some of its energy has been dispersed to the ice and water. However, as calculated in the example, the entropy of the system of ice and water has increased more than the entropy of the surrounding room has decreased. In an isolated system such as the room and ice water taken together, the dispersal of energy from warmer to cooler always results in a net increase in entropy. Thus, when the 'universe' of the room and ice water system has reached a temperature equilibrium, the entropy change from the initial state is at a maximum. The entropy of the thermodynamic system is a measure of how far the equalization has progressed.

A special case of entropy increase, the entropy of mixing, occurs when two or more different substances are mixed. If the substances are at the same temperature and pressure, there will be no net exchange of heat or work - the entropy increase will be entirely due to the mixing of the different substances.[11]

From a macroscopic perspective, in classical thermodynamics the entropy is interpreted simply as a state function of a thermodynamic system: that is, a property depending only on the current state of the system, independent of how that state came to be achieved. The state function has the important property that, when multiplied by a reference temperature, it can be understood as a measure of the amount of energy in a physical system that cannot be used to do thermodynamic work; i.e., work mediated by thermal energy. More precisely, in any process where the system gives up energy ΔE, and its entropy falls by ΔS, a quantity at least TR ΔS of that energy must be given up to the system's surroundings as unusable heat (TR is the temperature of the system's external surroundings). Otherwise the process will not go forward.

In 1862, Clausius stated what he calls the “theorem respecting the equivalence-values of the transformations” or what is now known as the second law of thermodynamics, as such:

The algebraic sum of all the transformations occurring in a cyclical process can only be positive, or, as an extreme case, equal to nothing.

Quantitatively, Clausius states the mathematical expression for this theorem is as follows. Let δQ be an element of the heat given up by the body to any reservoir of heat during its own changes, heat which it may absorb from a reservoir being here reckoned as negative, and T the absolute temperature of the body at the moment of giving up this heat, then the equation:

\int \frac{\delta Q}{T} = 0

must be true for every reversible cyclical process, and the relation:

\int \frac{\delta Q}{T} \ge 0

must hold good for every cyclical process which is in any way possible. This is the essential formulation of the second law and one of the original forms of the concept of entropy. It can be seen that the dimensions of entropy are energy divided by temperature, which is the same as the dimensions of Boltzmann's constant (kB) and heat capacity. The SI unit of entropy is "joule per kelvin" (J•K−1). In this manner, the quantity "ΔS" is utilized as a type of internal energy, which accounts for the effects of irreversibility, in the energy balance equation for any given system. In the Gibbs free energy equation, i.e. ΔG = ΔH - TΔS, for example, which is a formula commonly utilized to determine if chemical reactions will occur, the energy related to entropy changes TΔS is subtracted from the "total" system energy ΔH to give the "free" energy ΔG of the system, as during a chemical process or as when a system changes state.

[edit] Microscopic definition of entropy (statistical mechanics)

Main article: Entropy (statistical thermodynamics)

In statistical thermodynamics the entropy is defined as the number of microscopic configurations that result in the observed macroscopic description of the thermodynamic system:

S = k_B \ln \Omega \!

where

kB is Boltzmann's constant 1.38066×10−23 J K−1 and
\Omega \! is the number of microstates corresponding to the observed thermodynamic macrostate calculated using the multiplicity function.

This definition is considered to be the fundamental definition of entropy (as all other definitions can be mathematically derived from it, but not vice versa).

In Boltzmann's 1896 Lectures on Gas Theory, he showed that this expression gives a measure of entropy for systems of atoms and molecules in the gas phase, thus providing a measure for the entropy of classical thermodynamics.

In 1877, thermodynamicist Ludwig Boltzmann visualized a probabilistic way to measure the entropy of an ensemble of ideal gas particles, in which he defined entropy to be proportional to the logarithm of the number of microstates such a gas could occupy. Henceforth, the essential problem in statistical thermodynamics, i.e. according to Erwin Schrödinger, has been to determine the distribution of a given amount of energy E over N identical systems.

Statistical mechanics explains entropy as the amount of uncertainty (or "mixedupness" in the phrase of Gibbs) which remains about a system, after its observable macroscopic properties have been taken into account. For a given set of macroscopic quantities, like temperature and volume, the entropy measures the degree to which the probability of the system is spread out over different possible quantum states. The more states available to the system with higher probability, and thus the greater the entropy. In essence, the most general interpretation of entropy is as a measure of our ignorance about a system. The equilibrium state of a system maximizes the entropy because we have lost all information about the initial conditions except for the conserved quantities; maximizing the entropy maximizes our ignorance about the details of the system.[12]

On the molecular scale, the two definitions match up because adding heat to a system, which increases its classical thermodynamic entropy, also increases the system's thermal fluctuations, so giving an increased lack of information about the exact microscopic state of the system, i.e. an increased statistical mechanical entropy.

[edit] Entropy in chemical thermodynamics

Main article: Chemical thermodynamics

Thermodynamic entropy is central in chemical thermodynamics, enabling changes to be quantified and the outcome of reactions predicted. The second law of thermodynamics states that entropy in the combination of a system and its surroundings (or in an isolated system by itself) increases during all spontaneous chemical and physical processes. Spontaneity in chemistry means “by itself, or without any outside influence”, and has nothing to do with speed. The Clausius equation of δqrev/T = ΔS introduces the measurement of entropy change, ΔS. Entropy change describes the direction and quantitates the magnitude of simple changes such as heat transfer between systems – always from hotter to cooler spontaneously.[13] Thus, when a mole of substance at 0 K is warmed by its surroundings to 298 K, the sum of the incremental values of qrev/T constitute each element's or compound's standard molar entropy, a fundamental physical property and an indicator of the amount of energy stored by a substance at 298 K.[14][15] Entropy change also measures the mixing of substances as a summation of their relative quantities in the final mixture.[16]

Entropy is equally essential in predicting the extent of complex chemical reactions, i.e. whether a process will go as written or proceed in the opposite direction. For such applications, ΔS must be incorporated in an expression that *******s both the system and its surroundings, Δ Suniverse = ΔSsurroundings + Δ S system. This expression becomes, via some steps, the Gibbs free energy equation for reactants and products in the system: Δ G [the Gibbs free energy change of the system] = Δ H [the enthalpy change] – T Δ S [the entropy change].[14]

[edit] The second law

Main article: Second law of thermodynamics

An important law of physics, the second law of thermodynamics, states that the total entropy of any isolated thermodynamic system tends to increase over time, approaching a maximum value; and so, by implication, the entropy of the universe (i.e. the system and its surroundings), assumed as an isolated system, tends to increase. Two important consequences are that heat cannot of itself pass from a colder to a hotter body: i.e., it is impossible to transfer heat from a cold to a hot reservoir without at the same time converting a certain amount of work to heat. It is also impossible for any device that can operate on a cycle to receive heat from a single reservoir and produce a net amount of work; it can only get useful work out of the heat if heat is at the same time transferred from a hot to a cold reservoir. This means that there is no possibility of a "perpetual motion" which is isolated. Also, from this it follows that a reduction in the increase of entropy in a specified process, such as a chemical reaction, means that it is energetically more efficient.

In general, according to the second law, the entropy of a system that is not isolated may decrease. An air conditioner, for example, cools the air in a room, thus reducing the entropy of the air. The heat, however, involved in operating the air conditioner always makes a bigger contribution to the entropy of the environment than the decrease of the entropy of the air. Thus the total entropy of the room and the environment increases, in agreement with the second law.

[edit] Entropy balance equation for open systems

In chemical engineering, the principles of thermodynamics are commonly applied to "open systems", i.e. those in which heat, work, and mass flow across the system boundary. In a system in which there are flows of both heat (\dot{Q}) and work, i.e. \dot{W}_S (shaft work) and P(dV/dt) (pressure-volume work), across the system boundaries, the heat flow, but not the work flow, causes a change in the entropy of the system. This rate of entropy change is \dot{Q}/T, where T is the absolute thermodynamic temperature of the system at the point of the heat flow. If, in addition, there are mass flows across the system boundaries, the total entropy of the system will also change due to this convected flow.
During steady-state continuous operation, an entropy balance applied to an open system accounts for system entropy changes related to heat flow and mass flow across the system boundary.
During steady-state continuous operation, an entropy balance applied to an open system accounts for system entropy changes related to heat flow and mass flow across the system boundary.

To derive a generalized entropy balanced equation, we start with the general balance equation for the change in any extensive quantity Θ in a thermodynamic system, a quantity that may be either conserved, such as energy, or non-conserved, such as entropy. The basic generic balance expression states that dΘ/dt, i.e. the rate of change of Θ in the system, equals the rate at which Θ enters the system at the boundaries, minus the rate at which Θ leaves the system across the system boundaries, plus the rate at which Θ is generated within the system. Using this generic balance equation, with respect to the rate of change with time of the extensive quantity entropy S, the entropy balance equation for an open thermodynamic system is:[17]

\frac{dS}{dt} = \sum_{k=1}^K \dot{M}_k \hat{S}_k + \frac{\dot{Q}}{T} + \dot{S}_{gen}

where

\sum_{k=1}^K \dot{M}_k \hat{S}_k = the net rate of entropy flow due to the flows of mass into and out of the system (where \hat{S} = entropy per unit mass).

\frac{\dot{Q}}{T} = the rate of entropy flow due to the flow of heat across the system boundary.

\dot{S}_{gen} = the rate of internal generation of entropy within the system.

Note, also, that if there are multiple heat flows, the term \dot{Q}/T is to be replaced by \sum \dot{Q}_j/T_j, where \dot{Q}_j is the heat flow and Tj is the temperature at the jth heat flow port into the system.

[edit] Entropy in quantum mechanics (von Neumann entropy)

Main article: von Neumann entropy

In quantum statistical mechanics, the concept of entropy was developed by John von Neumann and is generally referred to as "von Neumann entropy". Von Neumann established the correct mathematical framework for quantum mechanics with his work Mathematische Grundlagen der Quantenmechanik. He provided in this work a theory of measurement, where the usual notion of wave collapse is described as an irreversible process (the so called von Neumann or projective measurement). Using this concept, in conjunction with the density matrix he extended the classical concept of entropy into the quantum domain.

It is well known that a Shannon based definition of information entropy leads in the classical case to the Boltzmann entropy. It is tempting to regard the Von Neumann entropy as the corresponding quantum mechanical definition. But the latter is problematic from quantum information point of view. Consequently Stotland, Pomeransky, Bachmat and Cohen have introduced a new definition of entropy that reflects the inherent uncertainty of quantum mechanical states. This definition allows to distinguish between the minimum uncertainty entropy of pure states, and the excess statistical entropy of mixtures.[18]

[edit] Standard textbook definitions

Note that textbook definitions are not always the most helpful definitions, but they are an important aspect of the culture surrounding the concept of entropy.

* Entropy – energy broken down in irretrievable heat.[19]
* Boltzmann's constant times the logarithm of a multiplicity; where the multiplicity of a macrostate is the number of microstates that correspond to the macrostate.[20]
* the number of ways of arranging things in a system (times the Boltzmann's constant).[21]
* a non-conserved thermodynamic state function, measured in terms of the number of microstates a system can assume, which corresponds to a degradation in usable energy.[22]
* a direct measure of the randomness of a system.[23]
* a measure of energy dispersal at a specific temperature.[24]
* a measure of the partial loss of the ability of a system to perform work due to the effects of irreversibility.[25]
* an index of the tendency of a system towards spontaneous change.[26]
* a measure of the unavailability of a system’s energy to do work; also a measure of disorder; the higher the entropy the greater the disorder.[27]
* a parameter representing the state of disorder of a system at the atomic, ionic, or molecular level.[28]
* a measure of disorder in the universe or of the availability of the energy in a system to do work.[29]

[edit] Approaches to understanding entropy

[edit] Order and disorder

Main article: Entropy (order and disorder)

Entropy, historically, has often been associated with the amount of order, disorder, and/or chaos in a thermodynamic system. The traditional definition of entropy is that it refers to changes in the status quo of the system and is a measure of "molecular disorder" and the amount of wasted energy in a dynamical energy transformation from one state or form to another.[30] In this direction, a number of authors, in recent years, have derived exact entropy formulas to account for and measure disorder and order in atomic and molecular assemblies.[31][9][32][33] One of the simpler entropy order/disorder formulas is that derived in 1984 by thermodynamic physicist Peter Landsberg, which is based on a combination of thermodynamics and information theory arguments. Landsberg argues that when constraints operate on a system, such that it is prevented from entering one or more of its possible or permitted states, as contrasted with its forbidden states, the measure of the total amount of “disorder” in the system is given by the following expression:[32][33]

Disorder=C_D/C_I\,

Similarly, the total amount of "order" in the system is given by:

Order=1-C_O/C_I\,

In which CD is the "disorder" capacity of the system, which is the entropy of the parts contained in the permitted ensemble, CI is the "information" capacity of the system, an expression similar to Shannon's channel capacity, and CO is the "order" capacity of the system.[9]

[edit] Energy dispersal

Main article: Entropy (energy dispersal)

The concept of entropy can be described qualitatively as a measure of energy dispersal at a specific temperature.[34] Similar terms have been in use from early in the history of classical thermodynamics, and with the development of statistical thermodynamics and quantum theory, entropy changes have been described in terms of the mixing or "spreading" of the total energy of each constituent of a system over its particular quantized energy levels.

Ambiguities in the terms disorder and chaos, which usually have meanings directly opposed to equilibrium, contribute to widespread confusion and hamper comprehension of entropy for most students.[35] As the second law of thermodynamics shows, in an isolated system internal portions at different temperatures will tend to adjust to a single uniform temperature and thus produce equilibrium. A recently developed educational approach avoids ambiguous terms and describes such spreading out of energy as dispersal, which leads to loss of the differentials required for work even though the total energy remains constant in accordance with the first law of thermodynamics.[36] Physical chemist Peter Atkins, for example, who previously wrote of dispersal leading to a disordered state, now writes that "spontaneous changes are always accompanied by a dispersal of energy", and has discarded 'disorder' as a description.[37][13]

[edit] Entropy and Information theory

Main articles: Information entropy and Entropy in thermodynamics and information theory

In information theory, entropy is the measure of the amount of information that is missing before reception and is sometimes referred to as Shannon entropy.[38]. Shannon entropy is a very general concept which finds applications in information theory as well as thermodynamics. It was originally devised by Claude Shannon in 1948 to study the amount of information in a transmitted message. The definition of the information entropy is, however, very general, and is expressed in terms of a discrete set of probabilities pi. In the case of transmitted messages, these probabilities were the probabilities that a particular message was actually transmitted, and the entropy of the message system was a measure of how much information was in the message. For the case of equal probabilities (i.e. each message is equally probable), the Shannon entropy (in bits) is just the number of yes/no questions needed to determine the content of the message.

The question of the link between information entropy and thermodynamic entropy is a hotly debated topic. Many authors argue that there is a link between the two,[39][40][41] while others will argue that they have absolutely nothing to do with each other.[42]

The expressions for the two entropies are very similar. The information entropy H for equal probabilities pi = p is:

H=K\ln(1/p)\,

where K is a constant which determines the units of entropy. For example, if the units are bits, then K=1/\ln(2). The thermodynamic entropy S , from a statistical mechanical point of view was first expressed by Boltzmann:

S=k\ln(1/p)\,

where p is the probability of a system being in a particular microstate, given that it is in a particular macrostate, and k is Boltzmann's constant. It can be seen that one may think of the thermodynamic entropy as Boltzmann's constant, divided by ln(2), times the number of yes/no questions that must be asked in order to determine the microstate of the system, given that we know the macrostate. The link between thermodynamic and information entropy was developed in a series of papers by Edwin Jaynes beginning in 1957.[43]

The problem with linking thermodynamic entropy to information entropy is that in information entropy the entire body of thermodynamics which deals with the physical nature of entropy is missing. The second law of thermodynamics which governs the behavior of thermodynamic systems in equilibrium, and the first law which expresses heat energy as the product of temperature and entropy are physical concepts rather than informational concepts. If thermodynamic entropy is seen as including all of the physical dynamics of entropy as well as the equilibrium statistical aspects, then information entropy gives only part of the description of thermodynamic entropy. Some authors, like Tom Schneider, argue for dropping the word entropy for the H function of information theory and using Shannon's other term "uncertainty" instead.[44]

[edit] Ice melting example

Main article: disgregation

The illustration for this article is a classic example in which entropy increases in a small 'universe', a thermodynamic system consisting of the 'surroundings' (the warm room) and 'system' (glass, ice, cold water). In this universe, some heat energy δQ from the warmer room surroundings (at 298 K or 25 C) will spread out to the cooler system of ice and water at its constant temperature T of 273 K (0 C), the melting temperature of ice. The entropy of the system will change by the amount dS = δQ/T, in this example δQ/273 K. (The heat δQ for this process is the energy required to change water from the solid state to the liquid state, and is called the enthalpy of fusion, i.e. the ΔH for ice fusion.) The entropy of the surroundings will change by an amount dS = -δQ/298 K. So in this example, the entropy of the system increases, whereas the entropy of the surroundings decreases.

It is important to realize that the decrease in the entropy of the surrounding room is less than the increase in the entropy of the ice and water: the room temperature of 298 K is larger than 273 K and therefore the ratio, (entropy change), of δQ/298 K for the surroundings is smaller than the ratio (entropy change), of δQ/273 K for the ice+water system. To find the entropy change of our 'universe', we add up the entropy changes for its constituents: the surrounding room, and the ice+water. The total entropy change is positive; this is always true in spontaneous events in a thermodynamic system and it shows the predictive importance of entropy: the final net entropy after such an event is always greater than was the initial entropy.

As the temperature of the cool water rises to that of the room and the room further cools imperceptibly, the sum of the δQ/T over the continuous range, at many increments, in the initially cool to finally warm water can be found by calculus. The entire miniature "universe", i.e. this thermodynamic system, has increased in entropy. Energy has spontaneously become more dispersed and spread out in that "universe" than when the glass of ice water was introduced and became a "system" within it.

[edit] Topics in entropy

[edit] Entropy and life

Main article: Entropy and life

For over a century and a half, beginning with Clausius' 1863 memoir "On the Concentration of Rays of Heat and Light, and on the Limits of its Action", much writing and research has been devoted to the relationship between thermodynamic entropy and the evolution of life. The argument that life feeds on negative entropy or negentropy as put forth in the 1944 book What is Life? by physicist Erwin Schrödinger served as a further stimulus to this research. Recent writings have utilized the concept of Gibbs free energy to elaborate on this issue. In other cases, some creationists have argued that entropy rules out evolution.[45]

In the popular 1982 textbook Principles of Biochemistry by noted American biochemist Albert Lehninger, for example, it is argued that the order produced within cells as they grow and divide is more than compensated for by the disorder they create in their surroundings in the course of growth and division. In short, according to Lehninger, "living organisms preserve their internal order by taking from their surroundings free energy, in the form of nutrients or sunlight, and returning to their surroundings an equal amount of energy as heat and entropy."[46]

Evolution related definitions:

* Negentropy - a shorthand colloquial phrase for negative entropy.[47]
* Ectropy - a measure of the tendency of a dynamical system to do useful work and grow more organized.[30]
* Syntropy - a tendency towards order and symmetrical combinations and designs of ever more advantageous and orderly patterns.
* Extropy – a metaphorical term defining the extent of a living or organizational system's intelligence, functional order, vitality, energy, life, experience, and capacity and drive for improvement and growth.
* Ecological entropy - a measure of biodiversity in the study of biological ecology.

[edit] The arrow of time

Main article: Entropy (arrow of time)

Entropy is the only quantity in the physical sciences that "picks" a particular direction for time, sometimes called an arrow of time. As we go "forward" in time, the Second Law of Thermodynamics tells us that the entropy of an isolated system can only increase or remain the same; it cannot decrease. Hence, from one perspective, entropy measurement is thought of as a kind of clock. [citation needed]

[edit] Entropy and cosmology

Main article: Black hole thermodynamics

We have previously mentioned that a finite universe may be considered an isolated system. As such, it may be subject to the Second Law of Thermodynamics, so that its total entropy is constantly increasing. It has been speculated that the universe is fated to a heat death in which all the energy ends up as a homogeneous distribution of thermal energy, so that no more work can be extracted from any source.

If the universe can be considered to have generally increasing entropy, then - as Roger Penrose has pointed out - gravity plays an important role in the increase because gravity causes dispersed matter to accumulate into stars, which collapse eventually into black holes. Jacob Bekenstein and Stephen Hawking have shown that black holes have the maximum possible entropy of any object of equal size. This makes them likely end points of all entropy-increasing processes, if they are totally effective matter and energy traps. Hawking has, however, recently changed his stance on this aspect.

The role of entropy in cosmology remains a controversial subject. Recent work has cast extensive doubt on the heat death hypothesis and the applicability of any simple thermodynamic model to the universe in general. Although entropy does increase in the model of an expanding universe, the maximum possible entropy rises much more rapidly - thus entropy density is decreasing with time. This results in an "entropy gap" pushing the system further away from equilibrium. Other complicating factors, such as the energy density of the vacuum and macroscopic quantum effects, are difficult to reconcile with thermodynamical models, making any predictions of large-scale thermodynamics extremely difficult. [citation needed]

[edit] Miscellaneous definitions

* Entropy unit - a non-S.I. unit of thermodynamic entropy, usually denoted "e.u." and equal to one calorie per kelvin
* Gibbs entropy - the usual statistical mechanical entropy of a thermodynamic system.
* Boltzmann entropy - a type of Gibbs entropy, which neglects internal statistical correlations in the overall particle distribution.
* Tsallis entropy - a generalization of the standard Boltzmann-Gibbs entropy.
* Standard molar entropy - is the entropy content of one mole of substance, under conditions of standard temperature and pressure.
* Black hole entropy - is the entropy carried by a black hole, which is proportional to the surface area of the black hole's event horizon.[48]
* Residual entropy - the entropy present after a substance is cooled arbitrarily close to absolute zero.
* Entropy of mixing - the change in the entropy when two different chemical substances or components are mixed.
* Loop entropy - is the entropy lost upon bringing together two residues of a polymer within a prescribed distance.
* Conformational entropy - is the entropy associated with the physical arrangement of a polymer chain that assumes a compact or globular state in solution.
* Entropic force - a microscopic force or reaction tendency related to system organization changes, molecular frictional considerations, and statistical variations.
* Free entropy - an entropic thermodynamic potential analogous to the free energy.
* Entropic explosion – an explosion in which the reactants undergo a large change in volume without releasing a large amount of heat.
* Entropy change – a change in entropy dS between two equilibrium states is given by the heat transferred dQrev divided by the absolute temperature T of the system in this interval.[49]
* Sackur-Tetrode entropy - the entropy of a monatomic classical ideal gas determined via quantum considerations.

[edit] Other relations

[edit] Other mathematical definitions

* Kolmogorov-Sinai entropy - a mathematical type of entropy in dynamical systems related to measures of partitions.
* Topological entropy - a way of defining entropy in an iterated function map in ergodic theory.
* Relative entropy - is a natural distance measure from a "true" probability distribution P to an arbitrary probability distribution Q.
* Rényi entropy - a generalized entropy measure for fractal systems.

[edit] Sociological definitions

The concept of entropy has also entered the domain of sociology, generally as a metaphor for chaos, disorder or dissipation of energy, rather than as a direct measure of thermodynamic or information entropy:

* Entropology – the study or discussion of entropy or the name sometimes given to thermodynamics without differential equations.[6][50]
* Psychological entropy - the distribution of energy in the psyche, which tends to seek equilibrium or balance among all the structures of the psyche.[51]
* Economic entropy – a semi-quantitative measure of the irrevocable dissipation and degradation of natural materials and available energy with respect to economic activity.[52][53]
* Social entropy – a measure of social system structure, having both theoretical and statistical interpretations, i.e. society (macrosocietal variables) measured in terms of how the individual functions in society (microsocietal variables); also related to social equilibrium.[54]
* Corporate entropy - energy waste as red tape and business team inefficiency, i.e. energy lost to waste.[55] (This definition is comparable to von Clausewitz's concept of friction in war.)

[edit] Quotes
“ Any method involving the notion of entropy, the very existence of which depends on the second law of thermodynamics, will doubtless seem to many far-fetched, and may repel beginners as obscure and difficult of comprehension. ”

--Willard Gibbs, Graphical Methods in the Thermodynamics of Fluids (1873)

“ My greatest concern was what to call it. I thought of calling it ‘information’, but the word was overly used, so I decided to call it ‘uncertainty’. When I discussed it with John von Neumann, he had a better idea. Von Neumann told me, ‘You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, nobody knows what entropy really is, so in a debate you will always have the advantage. ”

--Conversation between Claude Shannon and John von Neumann regarding what name to give to the “measure of uncertainty” or attenuation in phone-line signals (1949)

exactlythesame
09-16-2007, 06:54 PM
did you know you can't destroy energy

BumbleBeeMouth
09-16-2007, 07:04 PM
Main article: Black hole thermodynamics

We have previously mentioned that a finite universe may be considered an isolated system. As such, it may be subject to the Second Law of Thermodynamics, so that its total entropy is constantly increasing. It has been speculated that the universe is fated to a heat death in which all the energy ends up as a homogeneous distribution of thermal energy, so that no more work can be extracted from any source.

If the universe can be considered to have generally increasing entropy, then - as Roger Penrose has pointed out - gravity plays an important role in the increase because gravity causes dispersed matter to accumulate into stars, which collapse eventually into black holes. Jacob Bekenstein and Stephen Hawking have shown that black holes have the maximum possible entropy of any object of equal size. This makes them likely end points of all entropy-increasing processes, if they are totally effective matter and energy traps. Hawking has, however, recently changed his stance on this aspect.

The role of entropy in cosmology remains a controversial subject. Recent work has cast extensive doubt on the heat death hypothesis and the applicability of any simple thermodynamic model to the universe in general. Although entropy does increase in the model of an expanding universe, the maximum possible entropy rises much more rapidly - thus entropy density is decreasing with time. This results in an "entropy gap" pushing the system further away from equilibrium. Other complicating factors, such as the energy density of the vacuum and macroscopic quantum effects, are difficult to reconcile with thermodynamical models, making any predictions of large-scale thermodynamics extremely difficult.


Ah thank ye. It seems that they dont really know/cant bear to apply one law to the one division.

tcm
09-16-2007, 07:06 PM
did you know you can't destroy energy
actually my "friends" call me mr. buzzkill.

BumbleBeeMouth
09-16-2007, 07:15 PM
So much potential though.

mayday
09-16-2007, 11:21 PM
the history channel just finished the birth and life of Earth and it was excellent. everyone should watch it

selection7
09-17-2007, 04:32 AM
Hmmm. I agree with the point that stardom moves you farther from the things that originally make you a success. It's something I've thought about before...for some reason Bob Dylan always pops into my head when I get to thinking about it (but that's not important). But I think you're getting too caught up in the "can't relate to the average Joe anymore". Maybe it's true, but relating to the average Joe isn't what made Billy great, it was being able to channel his creativity into what moved him and excited him specifically about music. Don't worry about how his new perspectives affect his lyrics. I've got news for you; there's no lyrics that could be written that would turn Zeitgeist into an MCIS or SD.

Does any music excite and cause Billy to obsses over it like he did in his youth? Somehow I doubt it. All those years (pre-success) were important because every one of them were building blocks for what he would eventually have to offer the world as a musician. Simply becoming a star doesn't have to mean you've stopped "building blocks". Like that other post suggested, Billy has led a very eventfull life since becoming successful, but his frame of reference has changed, and with that he nevertheless runs such a risk.

When I listen to Zeitgeist I find it hard to believe that such songs were what he dreamed of creating back when he was hanging out under bridges with hookers and bathing once every two weeks. In essence, I'm saying he's lost connection with something special within himself, not within us. And Billy is a tremendously persuasive example of this sort of thing because he's clearly still ridiculously talented, but now consistantly makes decisions of questionable taste...even though back in the day, the man could almost literally do no wrong. I'm sure Jimmy is of great help to Billy, but he's clearly not enough (in terms of perspective and good taste).

darthjul
09-17-2007, 01:50 PM
I find Bill's work post-Mellon Collie just as engaging as any of the earlier stuff that everyone else seems so connected to. He has said himself that if the songs seem less personal its because he fells colder in his own life as a result of everything that has transpired in the resulting years.
The songs themselves are no less well written, hell I'd say some are better. But the impact they have is diminished by the fact that even in ten years, we've become jaded by how much access we have to music and art. The new stuff may seem less vibrant because we have a good frame of reference of what to expect. Will the next Radiohead album have the same impact as OK or Kid A? Hell no, cause we have a fair idea of what they are capable of. Even were they to release an amazingly bold and crazy album, most people could just say... "Ah.. well, thats what we expect from them." Just a theory.

darthjul
09-17-2007, 01:53 PM
WHat I'm trying to say is, there was a time when we didn't have the Pumpkins. They came, kicked our asses collectively and now we have that expectation everytime. So the ass kicking is lessened each time. For some.

Glenna Glynis
09-17-2007, 02:26 PM
yes Billy is aging and his prospective is changing with that. We are also aging and changing, we are not the same people we used to be, so our perspective has changed as well. We are now all moving in different directions. As we grow older we become less impressionable and desensitized to pain and suffering. We grow numb, cold and old. The reference points we once judged distance from has moved and changed. 1995 has come and gone, were all just trees bent by the wind, that no longer blows. That being said I think Zeit is a solid album and has a few songs on it that may even musically top some classics, but we are numb and resistant, we want to feel the way we felt in 1995 and we blame Billy for changing, but we have changed too.

mayday
09-17-2007, 03:11 PM
i dont want to feel like i did in 1995. im 12 years older and all the better for it and i cant wait for whats next. so speak for yourself!

Glenna Glynis
09-17-2007, 04:54 PM
I was speaking from my prespective to the older fans who are always tring to figure out why the music may feel a little hollow. "the more you change the less you feel?" I hope the pumpkins keep drawing new fans like yourself and keep making great music.

mayday
09-17-2007, 05:19 PM
new fan lol... i've been a fan for 13 years but yeah I think the new music is great

selection7
09-17-2007, 05:36 PM
You suggest there's little difference between the quality of the music mid-90's and today, and the differences in us are the real issue. No. I don't believe that for a second. And I totally recognize that I've changed.

Also, the very next post after mine went on about the music seeming less "personal" and more "cold". The whole point of my post was to influence people to stop getting hung up on that. Again, it's not about us or a connection to us, or the lyrics that some of you apparently identified with so much from the mid-90's (I sure didn't). When Billy makes incredible music, people will know it, we won't be confused by lyrics that somehow seem less emo.

exactlythesame
09-17-2007, 06:33 PM
Main article: Black hole thermodynamics

We have previously mentioned that a finite universe may be considered an isolated system. As such, it may be subject to the Second Law of Thermodynamics, so that its total entropy is constantly increasing. It has been speculated that the universe is fated to a heat death in which all the energy ends up as a homogeneous distribution of thermal energy, so that no more work can be extracted from any source.

If the universe can be considered to have generally increasing entropy, then - as Roger Penrose has pointed out - gravity plays an important role in the increase because gravity causes dispersed matter to accumulate into stars, which collapse eventually into black holes. Jacob Bekenstein and Stephen Hawking have shown that black holes have the maximum possible entropy of any object of equal size. This makes them likely end points of all entropy-increasing processes, if they are totally effective matter and energy traps. Hawking has, however, recently changed his stance on this aspect.

The role of entropy in cosmology remains a controversial subject. Recent work has cast extensive doubt on the heat death hypothesis and the applicability of any simple thermodynamic model to the universe in general. Although entropy does increase in the model of an expanding universe, the maximum possible entropy rises much more rapidly - thus entropy density is decreasing with time. This results in an "entropy gap" pushing the system further away from equilibrium. Other complicating factors, such as the energy density of the vacuum and macroscopic quantum effects, are difficult to reconcile with thermodynamical models, making any predictions of large-scale thermodynamics extremely difficult.


Ah thank ye. It seems that they dont really know/cant bear to apply one law to the one division.

entropy is invincible

BumbleBeeMouth
09-17-2007, 06:52 PM
prespective prospective perspective

Can you make your mind up please.

Rarely
09-17-2007, 08:14 PM
ban
agreed