Redefining the black holes

Recently, both Nature (Stephen Hawking: 'There are no black holes') and New Scientist (Stephen Hawking's new theory offers black hole escape)  covered Hawking's recent paper, Information Preservation and Weather Forecasting for Black Holes, discussed earlier on this blog. Since then, I've seen several times articles re-blogging the idea that Hawking said there are no black holes. Some hurried to say that Hawking considers this his "greatest blunder" (making reference to Einstein's regret that he conjectured the existence of dark energy for the wrong reasons, this preventing him to realize the expansion of the universe).

What Hawking said in fact was that

The absence of event horizons mean that there are no black holes - in the sense of regimes from which light can't escape to infinity.

But he continues that black holes exist, but they are not as he originally defined them:

There are however apparent horizons which persist for a period of time. This suggests that black holes should be redefined as metastable bound states of the gravitational field.

After a regular person makes a claim about something, he hardly changes his mind. Especially since that claim is part of what made him famous. We find difficult to withdraw our positions, because we are afraid to look weak. One reason I admire Hawking is that he had in several occasions the courage to change his mind, and even to admit he was wrong. He made several bets with his fellows Kip Thorne and John Preskill, concerning the existence of black holes, of naked singularities, and regarding the information loss. He eventually conceded all these bets, even though no clear cut evidence was discovered for either of the sides.

Hawking's first great discovery was the big bang singularity theorem, according to which the universe started from a singularity. It is difficult to later reject the very thing that made you famous in the first place, but Hawking, together with James Hartle, replaced the initial singularity with the famous no-boundary proposal, which doesn't have this singularity (although, technically, the positive defined metric they put at the beginning of the universe is separated by the Lorentzian one by a space slice which is in fact singular).

At various points of his career, Hawking expresses his doubts about string theory. For instance, in his debate with Penrose, he said

I think string theory has been over sold.

and

it seems we don’t need string theory even for the beginning of the universe.

 and

If this is true it raises the question of whether string theory is a genuine scientific theory. Is mathematical beauty and completeness enough in the absence of distinctive observationally tested predictions. Not that string theory in its present form is either beautiful or complete.

But in few years, he became a major supporter of string theory, as follows from this paper and this book.

Arguably, most of the fame of Hawking comes from his results concerning the black holes. But I don't think it is true as it is claimed now that, after a lifetime dedicated to the study of black holes, he arrived at the conclusion that they don't exist. He only rejects the existence of black holes defined as objects surrounded by event horizons, defined in their turn in a particular way. And in fact, he rejects that notion of event horizon. The notion of event horizon exists for long time, but at some point, Hawking redefined it, as the surface separating the points in spacetime which can't be seen from the future null infinity. Before that, the event horizon was known from stationary black holes, like the Schwarzschild, the Reissner-Nordström, and the Kerr-Newmann ones, and was generalized to trapped null surfaces. Hawking opposed to this general definition, because it would depend on the observer. Such apparent horizons are therefore not invariant, and Hawking proposed a global definition. The problem with the global definition is that it depends on the entire future, to establish whether a given point will eventually be visible from the null infinity or not. But if the black holes evaporate in a way compatible with the AdS-CFT conjecture, they have to respect the CPT symmetry. Since a global notion of event horizon violates this symmetry, Hawking proposes to reject it.

Hawking did not change his mind about the existence of the black holes, but only about his own definition of black holes, as those regions in spacetime which can't be seen from the future null infinity. He proposes instead to consider again the black holes to be regions surrounded by apparent horizons.

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.