Thursday, January 23, 2014

Hawking breaks the firewall

Hawking finally uploaded the paper containing his Skype talk at the Fuzz or fire workshop, named Information Preservation and Weather Forecasting for Black Holes. The paper, whose body has two pages, is an almost verbatim transcription of the 9' talk, with a tiny paragraph inserted before the final one. The talk was very dense, with great qualitative arguments, but almost no quantitative ones, and I kind of hoped that the paper will be more detailed in this respect.

The first argument Hawking brought against firewalls is that 
if the firewall were located at the event horizon, the position of the event horizon is not locally determined but is a function of the future of the spacetime.
Hawking defined long time ago the event horizon as being the surface separating the events that will eventually be seen from the future infinity, from those that will never be. Thus, we can know the event horizon only if we know the entire future history of the universe.This rules out any special structure which one may try to attach to the horizon, being it firewalls, stretched horizons, bits containing the information from the black hole etc. This argument is technically correct, but this doesn't rule out alternative local definitions of the horizon, and on which the firewall may live. I think this argument comes from the usage of different definitions.

 One thing I find particularly intriguing is that Hawking doesn't discuss the singularities. Singularities are predicted by Penrose's black hole singularity theorem, which inspired Hawking in coming up with  his own big bang singularity theorem. Also singularities are a necessary part of Hawking's original argument for the information loss. So, it is a bit strange that he doesn't say much about them. Well, he referred to the paper in which he proposed the resolution of the information paradox, and said that "the correlation functions from the Schwarzschild anti deSitter metric decay exponentially with real time". So, he considers that the contribution from the Schwarzschild singularities is negligible.

I find more interesting Hawking's argument that the ADS-CFT correspondence requires the black holes to be symmetric in time:
the evaporation of a black hole is the time reverse of its formation (modulo CP), though the conventional descriptions are very different. Thus if one assume quantum gravity is CPT invariant, one rules out remnants, event horizons, and firewalls.
Of course, again, one can imagine a way by which the firewalls are time symmetric, and use a different definition of the event horizon. But the reason I find interesting this argument of Hawking is that it doesn't preclude singularities, only the singularities that are not time symmetric. For instance, fig. A. depicts the Penrose diagram of the evaporating black hole that is not time symmetric, while fig. B. depicts a time symmetric one, obtained by analytic extension beyond the singularity. I give more details about this in Black Hole Information Paradox 3. Look for the information where you lost it.
A. Penrose diagram for the evaporating black hole, standard scenario.
B. Penrose diagram for the evaporating black hole, when the solution is analytically extended through the singularity (as in arXiv:1111.4837). In the new solution, the geometry can be described in term of finite quantities, without changing Einstein's equation. Fields can go through the singularity, beyond it.
So, I think Hawking's argument based on the ADS-CFT correspondence is compatible with the approach to the black hole singularities which I proposed, and excludes the standard solution, which is not time symmetric.

No comments: