Black Holes as 2 Dimensional Objects

fzero

The Kruskal coordinates are "geodesically complete," which is explained in the last paragraph at http://en.wikipedia.org/wiki/Kruskal...ekeres_diagram. The Schwarzschild coordinates are fine for the external observer, who only has access to the region outside the horizon. For the infalling observer, the coordinate singularity in the Schwarzschild variables makes them poorly suited, so Kruskal coordinates are more suitable.

This is an unusual statement. Most physical systems have data that is most easily described by specifying it with variables that depend on the volume. For example, if we have a box of ideal gas, using the positions and momenta of the gas particles suggests that the entropy depends on the volume of the box, c.f. http://hyperphysics.phy-astr.gsu.edu...entropgas.html. It is considered unusual that the entropy of a black hole only depends on its surface area. This fact is thought to have deep implications for what properties a theory of quantum gravity must have http://en.wikipedia.org/wiki/Holographic_principle.

Both the questions of what happens at a gravitational singularity and why the black hole information depends on surface area rather than volume are considered to be in the realm of quantum gravity. There is presently no complete answer to these questions.

Vastin

Indeed, the Holographic Principle is precisely what got me started on this entire re-examination of the black hole.

Up until I read about GEO 600 results , I hadn't really put much thought into it, but the moment I got what they were getting at, I started thinking about where one would go about finding a two dimensional surface in the universe at large, and a black-hole event horizon was the only ready candidate. Then I began trying to sort out the information storage problems inherent in a singularity, and ended up becoming dissatisfied with the commonly accepted model.

I remain dissatisfied. I will freely admit that my mathematics aren't good enough to properly comprehend the space-time geometries we've been discussing - but I think my grasp of information theory is good enough to tell me that you can't compress data into a singularity by any currently accepted theory - so much so that I feel it must cast suspicion back on any theory that posits such a singularity in the first place.

Given the sheer amount of data and entropy in a black hole, a VAST amount of processing is going on there, over an exorbitant period of time. But how can you process anything in a singularity? I'm fairly certain you can't. It should be essentially inert - thus the search for a solution at the event horizon itself, rather than within.

Vastin

http://en.wikipedia.org/wiki/Bekenstein_bound

Ah, here we go. It's mainly volume bound, not surface area bound, though in the case of black holes, the surface area does happen to be a perfect bound for the amount of mass/data contained. Given that they are the densest things in the universe, that's close enough, though it doesn't neatly match with my earlier statements. Learning as I go here. ;)

I guess I should simply state that I currently have a higher confidence in this boundary than I do in current gravitational theorem, the topographies we've been discussing, or in any theory that posits infinite informational density or the inscription of data without the corresponding mass/energy to describe it.

SpiffyKavu

fzero, I like your explanations here, but I must point out that the Kruskal-Szekeres coordinate chart is not geodesically complete, but rather maximally extended. There is still the past and future singularities where geodesics can end, though there do exist geodesics which are themselves complete: they extend to infinite proper time in both the positive and negative directions.

And Vastin, have you read Susskind's book "The Black Hole War"? It discusses all of these issues you've brought up and it is aimed at a general audience. Of course, Susskind is biased, so I take him with a grain of salt. But he does say some interesting things.

And have you also read about Hawking's and Penrose's singularity theorems? It basically states that singularities are guaranteed in general relativity inside black holes and at the big bang, given certain requirements. Of course this ignores all quantum effects, which is thought to take over at small scales. It is often hoped that these unknown quantum effects would serve to prevent the formation of a singularity.

Vastin

It sounds like I have some fun reading to do. :)

While I know the favored existing theorems posit singularities, there is still some real uncertainty about whether they'll hold up through further development of quantum theory - or as you suggest, they may hold up in general, but quantum phenomena may act to block singularity formation regardless.

My bet is on the latter, because the violation of information principles seems to me an intractable problem that is unlikely to be resolved so long as mass is permitted to compact into a singularity. Ergo, there is likely another outcome.

Hawking's admission that black holes likely evaporate their information back out into the universe without destroying it makes the case for this considerably stronger, because again, if it was being compacted into a singularity, it is hard to posit a mechanism that would allow for that information to continue to exist in the interim - unless you want to consider time reversal, and I'm not ready to swallow that one yet either...

I'm not suggesting that the theory that describes all those possible phenomena are wrong, but I'm willing to bet that other factors will inevitably arise to assure they are never realized. Like imaginary numbers, they'll be useful to play with in theoretical terms, but they will never exist.

In any case, we've basically got this super-massive object with both an ideal data storage threshold AND the what appears to be the highest processing power in the universe (as suggested by its entropy) - so some process is going on there that is vastly more complex than any singularity should allow. I'll frankly be rather disappointed if they turn out to be little more than the universe's most thorough wood-chippers.

fzero

This is probably not a good attitude to have. General relativity has been well-tested from terrestrial to cosmological scales, and is in excellent agreement with experiment. We should view singularities as something whose correct description will require something beyond general relativity, presumably a theory of quantum gravity. This is not a reason to have lower confidence in GR: we simply must recognize it's limitations.

In constrast, all other theories about black holes, from the Bekenstein-Hawking entropy, to the membrane paradigm and the holographic principle are complete speculation. Sure, some of it (esp. the BH entropy) are extremely well-motivated conjecture, but none of it has been tested. This is not a reason to discount it, as many of the ideas are worthy of further study. But it would be folly to believe in them at the expense of something that's as well-grounded as GR. In fact, almost all of the motivations for the speculative ideas involve agreement with GR in the appropriate limits.

fzero

You are correct, I wasn't being careful enough with the definition of the term. I linked to the (better than my own) discussion at the wiki in the hope that anyone reading what I wrote would get a more accurate summary. Thanks.

twofish-quant

Also it's very important to emphasize that this is a calculation trick, and not a description of reality.

twofish-quant

Which is more accurate polar coordinates or cartesian coordinates?

In fact you use the coordinate system that works based with your problem. If you use polar coordinates, you just have to realize that you will have problems doing calculations near r=0.

Join the club :-) :-) :-) It bothers a lot of people.

Suffice to say that enough people have tried to avoid the problem that if there was a simple way of avoiding the problem, we would have found it by now.

Something else that bothers people. It's called the black hole information paradox. One thing is that the rules of quantum mechanics says that information can't be destroyed. But black holes seem to destroy information.........

Also there are some very interesting linkages between computer science and black holes. Entropy.

Maybe. That's one of the ideas that resolves the paradox. However, that resolution happens to lead to some disturbing conclusions.

http://arxiv.org/abs/hep-th/0208013

The problem is that if information gets encoded into an event horizon going into the black hole, then it will get encoded in all event horizons. Now we know that the universe is accelerating so eventually everything is going to fall through an event horizon. Now if information gets encoded on that event horizon, then the total amount of information in the universe is going to stay constant. If that happens then the universe is destined to repeat itself.

Notice the strings of "if's". The point of the paper is that if you don't want the conclusion, then one of the "if's" is wrong.

The idea is that ***from the point of view of an outside observer*** (and I have to emphasize that), things appear to "freeze" at the event horizon, and so you have some "frozen information".

At that point you have to ask "what is information?" ***From the point of view of an outside observer*** things appear to freeze when you cross the event horizon, and you can use that to store information. The fact that in fact this is something of an optical illusion doesn't change the fact that information is stored.

fzero

I chose that as a safe example. It's clear that there is probably a more complete description of the black hole in terms of horizon degrees of freedom, going far beyond the original membrane paradigm. The AdS/CFT correspondence suggests that there are gravitational systems where a precise and complete description of a bulk geometry is given in terms of degrees of freedom on a surface of one less dimension. Given that this is the Astrophysics forum, I didn't feel it appropriate to derail too much.

Incidentally, since you relinked that page, I should take the opportunity to recommend Kip Thorne's Black Holes and Time Warps: Einstein's Outrageous Legacy to the OP. I haven't read the Susskind book that SpiffyKavu recommended, but I'm sure that's a good choice too. Thorne's book must be a bit dated in comparison, but still well worth a read for the quality and historical interest.

twofish-quant

You aren't the only one. Pretty much everyone is dissatisfied with the idea of a singularity. It's coming up with a better idea that's a problem.

Yup. We are pretty sure that theory breaks down at the singularity.

The trouble with that is that the event horizon isn't a physical location. A good analogy would be earth horizons. You have a different horizon based on where you are located on the earth, and because different people have different horizons you can say that nothing special happens at the horizon because your horizon isn't someone else's.

Similarly different people will have different "event horizons". The "event horizon" for someone falling into the black hole will be different from the horizon of a different observer. Because the location of the horizon is as property of the observer as much as it is a proper of the black hole, it's hard to argue that "something special" happens at the "event horizon for distant observers which is not the event horizon for someone falling in."

twofish-quant

And it's pretty clear that the true theory of gravity is something similar to GR. One problem with assuming something weird happens at the event horizon is that the strength of the gravity isn't that high so something weird that happens at the event horizon would presumably cause something weird to happen in other situations.

The other problem is that "how does gravity know that it's in an event horizon." So we have a theory of gravity that behaves exactly like GR outside of the event horizon, but then goes nuts the moment you move inside. But gravity has no way of knowing that it's inside the event horizon or outside, and having gravity behave differently based on where you are, causes lots of problems.

Oh yes. It's cool weird stuff, but it don't have a black hole nearby that I can test things with. Conversely I can check GR because my GPS works.

twofish-quant

The situation is that the existing theories posit singularities, therefore there is something wrong with the existing theories.

One other thing is that this is a good line of research since "thinking about information" seems at least to me to be the most viable way of getting us to a quantum theory of gravity. It seems to be to be a lot more productive than string theory.

Also you might want to add John Archibald Wheeler to your reading list. He is the person that came up with the idea of black holes, and he came up with a lot of odd ideas about information and black holes.

Real numbers don't exist either. Once consequence of thinking of the universe in terms of information theory is that it "digitalize" the universe meaning that the fundamental rules of the universe are based on integers and not real numbers.

One caveat. There was an author that mentioned that it was common to think of the universe based on the prevailing technology. We are surrounded by computers so we tend to think of the universe as a computer just like people in the 18th century thought of the world in terms of clocks. But the universe may be totally unlike a computer.

twofish-quant

The reason I said that this was a calculation trick is that there is genre of "crankish papers" that argue that black holes don't exist because time freezes at the event horizon. I didn't want an informed newbie to be led astray.

I'm a big fan of the membrane paradigm because it allows non-GR specialists to think about situations when GR is involved.

Vastin

Yeah, I'm really not trying to contest GR - my GPS works too. ;)

But I am trying to determine if there are domains where it is not as accurate as we would like, or possibly separate/related phenomena that prevents matter in a high density (near plank length) configuration from behaving as we expect as it attempts to pass through such a gravity field.

Basically, it's not so much the behavior of gravity I'm concerned with here - it's the behavior of matter. If, as you say, the gravity at the event horizon is non-infinite, then in theory it could be counterbalanced by another force at that point, preventing that matter from falling further. If two very powerful forces of this sort are arrayed directly against each other, you might get the sort of plank shell configuration that would help us prevent data loss - the question is, do we have any candidates for the outward pressure?

Does matter, for example, have a state of final compression beyond which it cannot be pushed, regardless of the energy applied? It it possible that rather than resisting the essentially 'infinite' pressure it would face at the singularity point, that it manages to find an incompressible equilibrium resting at the edge of the event horizon in stable orbit with its light cone resting precisely on the horizon? I presume that light cones generally narrow as the gravitational field increases, and I'm guessing that under the correct conditions that cone might be reduced to a line.

Vastin

I thought that the image trapped at the edge of an event horizon was red-shifted virtually out of existence and effectively invisible to any form of external detection?

Not sure what that means for the data it represents to be honest. The idea of the information being stripped 'off' of matter as it falls through the event horizon, so that 'information-less' mass is accreting into the singularity while its data is stored on the EH until such time as the mass is allowed to evaporate off, at which point it 'retrieves' its data from the EH on the way out.

That's a pretty exotic arrangement, and it doesn't even remotely protect us from the idea that something fantastic needs to happen at the EH boundary - it makes that event much weirder, as we have matter being stripped of almost all its properties except mass, with mass-less data being stored in the fabric of space-time and data-less mass falling into a singularity.

Ick.