LQC and the Information Paradox

[windy miller]

From my limited reading I get the impression that the bouncing black holes proposed by Rovelli and Vidotto implies a solution to the information paradox. The information comes back out when the bounce happens. But how does this relate to the idea of complimentarity? It seems the latter was the favoured solution at least until the firewall paradox was discovered but the said paradox puts complementarity in doubt.
So does the LQC solution imply there is no complimentarity or...?

 

[Haelfix]

So the information loss problem/firewall paper is essentially a no go theorem that forces you to abandon a cherished principle. As usually stated it forces you into choosing between giving up the unitarity of quantum mechanics, the validity of general relativity in low curvature regimes or the locality of the laws of physics.

Prefirewall paper the prevailing idea called black hole complimentarity provided a way out of that choice (backed up by some arguments coming from AdS/CFT), such that all three principles could still simultaneously hold true. However the firewall argument put serious strain on that solution, and forced physicists to revisit the problem.

Rovelli's solution violates the equivalence principle (so throws out GR as a solution in low curvature regimes) so as such it is not compatible with complimentarity (which keeps everything).

 

[windy miller]

Thanks very interesting,thanks for the reply. I am curious, the statement "Rovellis solution violates the equivalence principle" is that your own interpretation or does he say that as well ?

 

[Haelfix]

It's not an interpretation. The Schwarzschild solution is a vacuum solution to Einsteins field equation. Any proposed solution where someone sees a radiation field 'due to quantum mechanics' at the horizon after some elapsed proper time interval is a violation of the equivalence principle. These so called 'hot horizon' solutions (like the firewall itself) are all essentially in the same class.

https://backreaction.blogspot.com/2014/02/can-planck-stars-exist.html

 

[PeterDonis]

The Schwarzschild solution is a vacuum solution to Einsteins field equation.

Yes, but the Schwarzschild solution has a horizon whose area stays the same forever. Any time you start talking about black holes with horizon areas that can change, you're no longer talking about the pure Schwarzschild solution, or indeed about any pure vacuum solution. For the horizon area to change, there must be nonzero stress-energy somewhere. The stress-energy might be "effective" stress-energy due to quantum fields, but it has to be there.

 

[Haelfix]

It's actually a question of scale. One might ask whether Hawking radiation provides a counterexample. So in the semiclassical approximation we treat the Hawking radiation as a perturbation that does not backreact too much on the ambient background metric (which thus stays approximately Schwarzschild with an infinitesimal mass loss if you will, see Birrel and Davies).

This approximation breaks down exactly when the validity of effective field theory breaks down, (read when the size of the hole gets small and Planckian and the curvature invariants near the horizon start to get large).

In Rovellis paper, the perturbation is not small like normal Hawking radiation, it is large and classical before the point where you might expect the naive semiclassical approximation to breakdown. This implies that the near horizon of what an inertial observer sees is no longer Rindler, but something else... Hence a violation of the equivalence principle.

It's really the same general idea that a lot of people in the field have worked on. That the accumulation (Trickle) of small quantum mechanical modes might over time, provide a large backreaction effect and thus take you out of the semiclassical approximations straight jacket (where all of Hawking paradoxes appear). Still, you *are* macroscopically violating the classical theory if you do things too quickly and there are nogo theorems that address how this might work. There are quite a few good papers on this, going back to Don Page.
I like the following one by Mathur, where he explicitly goes through the 'evolution' iterations and shows how they stay within the validity of the semiclassical approximation:
https://arxiv.org/abs/0909.1038

 

[PeterDonis]

This approximation breaks down exactly when the validity of effective field theory breaks down

Sort of. Strictly speaking, once enough Hawking radiation has been emitted to reduce the hole's mass appreciably, you can no longer model the rest of the spacetime as vacuum, because it has to contain a not insignificant amount of mass/energy to compensate for the hole's loss. But it is true that as long as the emitted radiation can be approximated as spherically symmetric, it will have no effect on the spacetime curvature near the horizon.

(read when the size of the hole gets small and Planckian and the curvature invariants near the horizon start to get large)

But the point at issue is whether these two things--Planckian hole size and "large" curvature invariants near the horizon--are really equivalent. Since that's the point under dispute, you can't just assume it's true. I know many if not most experts in the field believe it's true, but has there been an ironclad proof?

 

[Haelfix]

But the point at issue is whether these two things--Planckian hole size and "large" curvature invariants near the horizon--are really equivalent. Since that's the point under dispute, you can't just assume it's true. I know many if not most experts in the field believe it's true, but has there been an ironclad proof?

That's correct, I am assuming the following statement to be true, and it is also true by assumption in the statement of the information loss paradox. Clearly it is true (semi)classically for an observer along one of those nice slices right?

In Schwarzschild coordinates one can calculate what an observer in free fall near the horizon sees, so eg he will only see the nonvanishing curvature components calculated in some orthonormal frame where the observer is momentarily at rest and will find roughly:
$$R(horizon) \sim \frac{1}{\left ( MG \right )^{2}}$$
So at the very least we must agree that if that inertial observer see's something different than this, he is no longer within the semiclassical approximation and measures a departure from the equivalence principle.

Rovelli's claim is that if you wait a certain time, shorter than the Page time, but still long enough for an accumulation to take place, then the horizon of a black hole is given by a different geometry (by construction), that he outlines in his paper. This thus falls into a class of solutions that evades the AMPS argument by denying one of the assumptions of the theorem.

 

[PeterDonis]

at the very least we must agree that if that inertial observer see's something different than this, he is no longer within the semiclassical approximation

If the semiclassical approximation includes the effective stress-energy tensor being vacuum, then yes, I agree. The obvious conclusion if an inertial observer saw something different would be that the effective stress-energy tensor was not vacuum.

and measures a departure from the equivalence principle.

I'm not sure this is true, because if the effective stress-energy tensor is not vacuum, then either the EP doesn't apply, or it applies but it predicts different observations from the vacuum case, depending on how strict a version of the EP you want to use.

This thus falls into a class of solutions that evades the AMPS argument by denying one of the assumptions of the theorem.

Because, as I understand it, the theorem assumes an effective vacuum stress-energy tensor. Basically the opposing arguments here, as I understand them, are "a black hole spacetime should be vacuum in the vicinity of the horizon, because quantum effects will be too small there to matter" vs "quantum effects are larger than everyone else thinks, so they can in fact change the effective stress-energy tensor so that it is no longer vacuum at or near the horizon".

 

[PeterDonis]

I like the following one by Mathur, where he explicitly goes through the 'evolution' iterations and shows how they stay within the validity of the semiclassical approximation:
https://arxiv.org/abs/0909.1038

I'm reading through this paper and I have a question. On p. 13 it says that the matter that originally collapsed to form the hole moves about 3 km away from the place where the pairs are being created at each stage of stretching. It basically seems to be assuming that there is an infinite amount of "room" inside the hole, along an r = const spacelike slice. I know this is true for the maximally extended Schwarzschild geometry--each r = const line (or sequence of 2-spheres if we include the angular coordinates) covers a range of $- \infty$ to $+ \infty$ in the $t$ coordinate, which is spacelike inside the horizon and so represents an infinite range of spatial distance.

However, I'm not sure it's true for the geometry actually discussed in the paper, which is only a portion of regions I and II of the maximally extended Schwarzschild geometry, joined to the collapsing matter, which is in turn a shell with a Minkowski interior. But the Minkowski interior has finite spatial extent in all three dimensions. So I don't see where there is infinite "room" inside the hole for the collapsing matter to move arbitrarily far away from the pair creation region.

 

[Haelfix]

Because, as I understand it, the theorem assumes an effective vacuum stress-energy tensor. Basically the opposing arguments here, as I understand them, are "a black hole spacetime should be vacuum in the vicinity of the horizon, because quantum effects will be too small there to matter" vs "quantum effects are larger than everyone else thinks, so they can in fact change the effective stress-energy tensor so that it is no longer vacuum at or near the horizon".

Yes, I concur! Actually many claim that quantum effects erase the singularity in some way, which then leads to an apparent horizon and some sort of communication of this information to the horizon. The problem is then how can local physics that occurs at the singularity (by assumption we are discussing huge galaxy wide black holes) possibly effect (due to quantum effects) the physics and temperature of a horizon (a global geometric quantity that involves knowing about the entire future history of all radiation that ever enters) far away in spacetime. You need highly nonlocal essentially acausal physics for that. It's wonderfully bizarre!

Your other question is a good one, I will study it when I get the chance.

 

[PeterDonis]

Actually many claim that quantum effects erase the singularity in some way, which then leads to an apparent horizon and some sort of communication of this information to the horizon.

I think there is also another option: that there is no event horizon at all, only an apparent horizon that forms and then eventually disappears.

The problem is then how can local physics that occurs at the singularity (by assumption we are discussing huge galaxy wide black holes) possibly effect (due to quantum effects) the physics and temperature of a horizon (a global geometric quantity that involves knowing about the entire future history of all radiation that ever enters) far away in spacetime.

By changing the future history of the spacetime--i.e., by changing the spacetime geometry, through changing the effective stress-energy tensor. At least one family of "bounce" models basically says that quantum gravity effects introduce an effective stress-energy tensor that is similar to dark energy, and by the time any collapsing object is dense enough to have formed an apparent horizon around itself, the dark energy effect is strong enough to halt the collapse and reverse it so that the curvature never becomes too large inside the apparent horizon and a singularity never forms. (The energy conditions are violated in this model, so it is not subject to the singularity theorems, which would otherwise require a singularity to form once an apparent horizon has formed.) Then the apparent horizon eventually disappears as the reversed collapse, i.e., expansion, distributes all the matter/energy back out. All of the events inside the "collapsed" region of spacetime can still send light signals to future null infinity (though they may take a long time to get there), so there is never an actual event horizon anywhere.

The same family of models, as I understand it, also says that Hawking radiation comes from apparent horizons, not event horizons; so the fact that there are no event horizons in these models does not invalidate the prediction of Hawking radiation, or the prediction that all of this stuff takes a very, very, very long time to happen, many orders of magnitude longer than the current age of the universe.

You need highly nonlocal essentially acausal physics for that.

I disagree. The models I described above involve only local physics. But local physics can affect global properties. In the standard collapse model where a singularity forms, an event horizon--a global property that depends on the entire future of the spacetime--is present because of purely local physics--how the collapsing matter collapses.

 

[Haelfix]

I'm reading through this paper and I have a question.
However, I'm not sure it's true for the geometry actually discussed in the paper, which is only a portion of regions I and II of the maximally extended Schwarzschild geometry, joined to the collapsing matter, which is in turn a shell with a Minkowski interior. But the Minkowski interior has finite spatial extent in all three dimensions. So I don't see where there is infinite "room" inside the hole for the collapsing matter to move arbitrarily far away from the pair creation region.

So I thought about this a bit, and I think you are right. Although its not critical to the argument, the angular part (S^2) is bounded and the question is how much space can you buy yourself by judicious choices of the spacelike slices and the mass M of the hole.
It clearly won't be infinity, but you can make it big (you can kinda see what I mean by redrawing the slices in figure 3 and deforming them slightly). It would be interesting to see if there was an expression for the maximum distance given that the spacelike slices are constrained by M/2 < r < 3M/2.

 

[Haelfix]

I think there is also another option: that there is no event horizon at all, only an apparent horizon that forms and then eventually disappears.

I disagree. The models I described above involve only local physics. But local physics can affect global properties. In the standard collapse model where a singularity forms, an event horizon--a global property that depends on the entire future of the spacetime--is present because of purely local physics--how the collapsing matter collapses.

A few things here. Having a singularity be resolved by quantum gravity and allowing an apparent horizon to form helps with the information loss paradox b/c in principle it allows the physics to be unitary (when you trace over the interior, you can purify the final asymptotic state).

Now, one could call this the 'black hole doesn't form' class of solutions to the information loss paradox.
Several problems though. 1) The singularity theorems are violated, requiring highly exotic matter at the cut out region near the singularity.
2) During the infall phase, you can reverse the argument and ask, what type of stress energy would you need in order NOT to produce a solution that possesses a global horizon, again with the assumption that GR is approximately valid far from the singularity.
I really enjoy Bill Unruh's take on that question, see here (first 7 minutes):

 

[PeterDonis]

Having a singularity be resolved by quantum gravity and allowing an apparent horizon to form helps with the information loss paradox b/c in principle it allows the physics to be unitary (when you trace over the interior, you can purify the final asymptotic state).

Yes, agreed.

one could call this the 'black hole doesn't form' class of solutions to the information loss paradox.

Yes.

The singularity theorems are violated, requiring highly exotic matter at the cut out region near the singularity.

Agreed. From what I've seen this is one of the main points of contention between the two camps--how bothered they are by the requirement of highly exotic matter.