If no singularity, what’s inside a big black hole?

genneth

I know... but that transform is non-trivial! E.g. the part of the world line of the infalling observer which is inside the horizon is not even in the spacetime of the asymptotic observer, so the transform must have some singularities; my question is whether they are physical. Searching for literature on this gives remarkably thin results (i.e. none). I really would like to know the answer, but I don't think anyone has it --- I would be happy to be shown otherwise.

Bernie G

BTW, maybe its not appropriate here, but I went to a talk a few days ago where the Nasa speaker said there may be far distant black holes with up to 10^12 solar masses. If true, thats about the equivalent of 1000 Milky Ways. Wow.

tom.stoer

I was only talking about the evaporation time compared to the time it takes for the infalling observer to cross the horizon; not to hit the singularity.

You only need a rough estimate.

The black hole evaporation time for a black hole of one solar mass (calculated based on Hawking radiation - which is definitly incorrect as soon as the hole becomes smaller and has Planck size) is approx. 10⁶⁷ years. Now think about an observer not located at infinity but e.g. at the earth orbit. The result is approx. the same (the gravity of the sun at the earth orbit is small, therefore time dilation due to the gravitational field is very small). And now think about this observer falling into the black hole. It will definity take less than 10⁶⁷ years ...

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

IttyBittyBit

tom.stoer, I think what genneth is getting at is that near the event horizon, gravitational time dilation increases without bound.

http://en.wikipedia.org/wiki/Gravita...otating_sphere

No matter how long it took for the black hole to evaporate, there is some finite distance from the event horizon where you would experience this time to be very short.

Think about it this way. As you fall into the event horizon, the Hawking radiation from the black hole is blue-shifted to such a high energy that it appears that the black hole is evaporating very quickly.

The statement 'you would not notice anything while falling into a large black hole' is not technically true. I would hardly call being blasted by intense gamma radiation, increasing in energy to infinity, 'not noticing anything'.

Of course, this is just a re-stating of the trans-Planckian problem. Which indicates the difficulty current physics has with event horizons. There are proposed solutions of course, fuzzball being one of them. At the end of the day you need some form of quantum gravity to explain event horizons adequately.

tom.stoer

That's true for a stationary observer but not for the infalling one. For him it takes finite proper time to cross the event horizon.

This is wrong! (the blue shift is correct but the effect is tiny)

There is no problem with event horizons in general relativity. They are well-understood and well-behaved.

All these proposals are attempts to resolve the singularity-issue. But there is no horizon-issue. They all agree that near the horizon of large black holes GR is still the correct low-energy limit.

Have you ever made a single calculation in general relativity by yourself?

genneth

Finite proper time if the horizon is eternal --- but the point is that it isn't.

Consider the following statements, and tell me where the logic goes off the rails:

1. An asymptotic observer never sees an infalling observer cross the event/dynamical horizon.
2. The horizon evaporates in a finite time.
3. The asymptotic observer will see the infalling observer still there after the horizon evaporates.
4. Therefore from the asymptotic observer's point of view, she doesn't cross the horizon either, and will live to see it completely evaporate.

This calculation can indeed be pushed all the way until the semi-classical approximation breaks down, and I think it's correct. I think this paper by Krauss (http://arxiv.org/abs/gr-qc/0609024 or Phys.Rev.D76:024005,2007) says the same thing, though I'm not sure I entirely agree with the details (event horizon vs. dynamical horizon, and therefore the interpretation).

(Btw, I am in no way invested in the original genesis of this problem --- I just think this scenario is worth thinking about as a thought experiment and might be informative on matters in general, not necessarily including the issue of what replaces a singularity...)

phinds

Only thing that occurs to me is that is would appear this argument requires the the two observers see the same event as though it were happening at the same time for both of them. I'm not sure I've said that right, but my point is that it seems to merge the two reference frames in a way that is not correct.

tom.stoer

The first flaw is that the asymptotic observer sees the infalling one approaching the horizon and standing still only if the horizon does not change. But as soon as you let the black hole evaporate the horizon will shrink and the infalling observer will no longer be frozen at the horizon.

The general flaw is that you mix two scenarios, namely arguments for a static spacetime with arguments for a dynamic spacetime with an evaporating BH.

The third flaw is that you don't calculate (or believe) what the infalling observer will actually see. The free-fall time is much smaller than the evaporation time.

suprised

This is not correct. Practically all important discussions and confusions turn around the horizon, and almost not at all around the singularity. The point seems to be that despite the horizon is weakly curved, quantum effects are strong and emphatically quantum gravity effects must play a crucial role there. The fuzzballs were invoked to implement the required macroscopic non-locality within string theory and this is definitely a horizon issue. Indeed in certain circumstances, quantum gravity effects are very relevant in the IR, while many approaches too naively just concentrate on the UV. The whole last week of our quantum gravity workshop was, in fact, devoted to precisely this issue.

tom.stoer

OK, maybe there is a "horizon-issue", but only in the sense that there is an underlying microscopic structure to classical spacetime.

Or do you think that classical GR (to which I refer when I am talking about free fall, proper time etc.) will no longer be valid outside the horizon for large black holes? Of course we expect that the evaporation will change, but we do not expect any "quantum effects" for classical motian, do we?

IttyBittyBit

Actually, no. That is only true if the infalling astronaut is very far from the horizon. If the infalling astronaut is near the horizon, the asymptotic observer will see them go in, but only at the very last moment where the black hole vanishes in a blast of Hawking Radiation. Therefore, from the asymptotic point of view, the infalling astronaut never spends any time 'inside' the event horizon. This is explained in this page: http://math.ucr.edu/home/baez/physic...s/fall_in.html

It seems you are right about this and I am wrong. I was thinking about a Schwarzschild reference frame. In such a reference frame you would see infinite blue-shift right before `going in'. However, a directly infalling observer would not see infinite blue-shift. Sorry for talking out of my a%$.

However, even though the blue-shift would not be infinite, it would still happen. It still remains that a theory of quantum gravity is needed before a definitive answer can be given. This paper talks about this subject at length: http://arxiv.org/abs/0806.0628

I've made many. If you know more about something than others, it is not appropriate to be rude about it.

tom.stoer

Thanks for the link.

Sorry about that!

Haelfix

Hmm. The problem isn't in the details of the dynamics but rather that the horizon analysis leads to the seemingly inescapable clash between two cherished physical principles, namely unitarity and locality whereby only one of the two can remain true in our universe.

Details about the small corrections due to quantum gravity cannot change this conclusion, which is why the information loss paradox is one of the greatest unresolved problems in theoretical physics. It isn't some mere detail of quantum gravity to be determined by future generations but rather the type of clash (like the UV catastrophe) that signals a theoretical underpinning must be altered (which qg must thereafter explain in detail microscopically)

So in a sense the answer is yes, the classical theory most likely is incomplete (even macroscopically), or rather it appears necessary for there to be a complementarity between descriptions and/or a dual holographic formulation that rescues us from what would otherwise be an absurdity.

suprised

This is absolutely correct; see eg the arguments of Mathur (eg recent papers/reviews) why "small" quantum gravity effects cannot help, rather they need to be of order one near the horizon. How this actually works in detail is a highly controversial issue, the fuzzball proposal ist just one attempt, though quite explicit and at least for me, quite convincing.

At any rate, issues of singularity resolution at the center appear to be a red herring to this problem, it is not the relevant question to ask.

atyy

So how big roughly would the macroscopic effects be at the horizon? If say a 70 kg person fell through the event horizon of a large black hole, would he notice anything like a fuzzball?

suprised

I guess, though this seems controversial, that the infalling observer experiences a coherent superposition of fuzzball states to the effect that he notices nothing particular at the horizon. I understand, though, that he infalling observer problem seems to be the weakest point in this proposal.

MTd2

This is why I don't believe in black holes. To make hawking radiation compatible to an asymptotic observer, an infalling observer would receive an infinitely strong blast of radiation when crossing the horizon. This is why I think the fuzzball is better than the LQG solution, at least how it is interpreted. The infinite blast should be actually the leaking gas of hot sphere made by whatever entity a fundamental theory of quantum gravity regards as fundamental.

EDIT.: Just noticed what suprised said above. So, what I mean is a killer fuzball.