Are black holes surrounded by firewalls?

Dilaton has noticed a new, extremely provocative concept that was introduced among the quantum gravity researchers two months ago: the firewall.



For decades, people teaching general relativity – including your humble correspondent (e.g. here) – have been explaining that nothing special happens to an infalling observer when she crosses a black hole event horizon. The curvature is usually pretty small there – the curvature radius is close to the black hole radius – and you only get torn apart once you approach the black hole singularity which may be much later.

Advertisement of a future text: Read also Raphael Bousso is right about firewalls

The event horizon is just a coordinate singularity; with a better choice of coordinates, the vicinity of the horizon (including a region below and a region above the horizon) looks like a nearly flat piece of the Minkowski spacetime. These coordinates may be "extremely distorted" functions of some other coordinates you may use for other purposes but they exist. Because the laws of general relativity are local, the (nearly) flat geometry of the region implies that there will be (nearly) the same phenomena there as in the flat space.

Later, some quantum properties of black holes have been pretty much established, too. The picture has made sense to everyone who has ever been considered a top expert in quantum gravity. That was the case until July 2012.




Let me first say what the quantum insights about black holes have been. The black holes evaporate and, as seen in AdS/CFT and Matrix Theory, it's still possible without any violation of the principles of quantum mechanics. So pure states evolve into pure states. From the viewpoint of the observers at infinity, a black hole is just another object with a discrete energy spectrum (well, the levels aren't really sharp because the black hole is unstable: they have a width) that effectively exists outside the event horizon only.

There may be an apparent contradiction between all these things and the validity of the effective field theory for low-energy processes but it's been believed that the contradictions go away because of the "black hole complementarity" paradigm, an opinion that the degrees of freedom (fields) inside the black hole aren't quite independent from those that are outside. They are complicated, scrambled functionals of them.

Now, in mid July 2012, four authors – two of whom are already established as quantum gravity black hole experts you don't want to overlook – published an explosive preprint called

Black Holes: Complementarity or Firewalls?

Joseph Polchinski, Donald Marolf, James Sully, and Ahmed Almheiri – sorry that I sorted the names from the most famous ones – decided to claim that after they have investigated some "detailed models" what happens with the information during the black hole evaporation, they concluded that the usual assumptions are mutually inconsistent, after all.

(See Joe Polchinski's guest blog at Cosmic Variance.)

They considered some thought experiments about entangled qubits that fall into the black hole - constructed out of the \(s\)-wave or other waves in the spherical harmonic decomposition – and decided that the only sensible conclusion is that when a black hole becomes "old" (i.e. when it emits or loses one-half of its initial Bekenstein-Hawking entropy), its event horizon gets transformed into a firewall that destroys everything that gets there.

(If you want to do an experiment, note that you will only be able to say "how you feel" after you cross the event horizon to those people who also fell into a black hole and whose lives are as doomed as yours.)



A song on several observers approaching a firewall. The musician suggests that it's only burning in the observer's eyes.

Within days, an emotional Leonard Susskind replied. The horizon may be kept intact; it's only the singularity of an old black hole that may need a make-up. In another day, Susskind released the second version of the manuscript. Two weeks later, he withdrew the paper because he "no longer believed the argument was right".

A week after the initial provocative paper, Raphael Bousso replied with a rather intelligent paper arguing why Polchinski et al. are wrong. It's clear that Raphael Bousso had to think it was wrong because he's really closer to classical general relativity and Polchinski et al. wanted to question its validity in environments that seem completely mundane! Bousso pointed out that Polchinski et al. were sloppy about the information that various observers, especially the infalling one, may access. When one realizes that they can only evaluate the "causal diamond", all the proofs of contradictions (which typically claim that one may xerox a quantum bit which must be impossible – or which clearly is impossible, depending on your goals – in every consistent quantum theory) become impossible.



Bousso's talk at Strings 2012 about this issue

Daniel Harlow posted another seemingly intelligent reply four days after Bousso. Polchinski et al. were sloppy when they were converting the observations from one observer's reference frame to another. However, Donald Marolf, a co-author of the original paper, kept on fighting and convinced Harlow that there was a hole in his argument. So Harlow withdrew the paper, just like Susskind. The topic of the black hole firewalls surely seems to be a firewall when it comes to burning the actual papers. ;-)



Great Firewall of China, by Ryan McLaughlin

But the fight for freedom and against firewalls continued. Yasunori Nomura, Jaime Varela, and Sean J. Weinberg argued in a way that is somewhat similar to Harlow: one must be careful when she constructs the map between the unitary quantum mechanics with the qubits on one side and the semiclassical world on the other side. The paper exists in the version v3 as well but unlike Harlow's paper, it hasn't been withdrawn yet.

Samir D. Mathur and David Turton "paradoxically" disagree with the firewall, too. I say it's "paradoxical" because Mathur is the father of fuzzballs which also "brutally change" the appearance of the black hole interior. However, they actually believe that the infalling observer has a complementary "nothing happens" description. Their explanation why Polchinski et al. are wrong is seemingly different again: Polchinski et al. assumed that an observer near the event horizon may say lots about the Hawking radiation even if he only looks outside the stretched horizon. Mathur and Turton say that he must actually go all the way to the real horizon and all the answers therefore depend on the Planckian physics.

Borun D. Chowdhury and Andrea Puhm picked catchy words for the same question: Is Alice burning of fuzzing? ;-) Among the followups, they're the closest ones so far to the original paper. They claim that all the critics of Polchinski et al. are just babbling irrelevant nonsense. The only exception are the fuzzball guys from the previous paragraph. Chowdhury and Puhm declare that it's important to get rid of the observer-centric description and talk about decoherence. When it's done, Alice burns when she is a low-energy packet but she may keep on living in the complementary fuzzball picture when she is a high-energy excitation. I suppose that for real people falling into a large, old black hole, this means that they're burned at stake.

In mid August, Leonard Susskind posted a new preprint, unusually similar to the previous one that was withdrawn weeks earlier. It's only the singularity that is modified for an old black hole. However, in the new paper, the evolution of the singularity is rather dramatic because it is – thanks to the growing entanglement – growing towards the event horizon and it ultimately overlaps with it. So Polchinski et al. are right that there's a firewall that burns you at that place; Susskind just says that it's more natural to call it a grown-up singularity, not an event horizon. He at least hopes that this only happens to old black holes (after the Page time, half entropy etc.), not after a much shorter scrambling time (which is just by a logarithmic factor longer than the black hole radius).

The debate wasn't stopped, of course. A day later, Iosif Bena, Andrea Puhm, and Bert Vercnocke formulated the question in yet another way: Non-extremal Black Hole Microstates: Fuzzballs of Fire or Fuzzballs of Fuzz? They take the fuzzball picture as a dogma and try to figure out how the interior looks to an infalling observer. Their conclusions seem inconclusive to me but they surely say lots of general and vacuous things that it could be an important research. ;-)

Amit Giveon and Nissan Itzhaki became supporters of the firewall when they decided to publish a related provocative concept: they think that string theory adds an extra degree of freedom, a zero mode, to the tip of the cigar (the counterpart of the event horizon in simple 1+1-dimensional examples of black holes) relatively to general relativity and this extra degree (or these extra degrees) of freedom may get generalized to a firewall that kills you what you fall into a higher-dimensional black hole.

Tom Banks and Willy Fischler use Tom's somewhat incomprehensible axiomatic framework, the holographic spacetime (I've been exposed to very intensely to as Tom's student), and they conclude that this axiomatic framework doesn't imply any firewalls.

Amos Ori prefers to assume that the semiclassical physics simply has to hold and adjusts any claims about the quantum information as necessary to agree with the primary assumption. With this attitude, he reaches a nearly comparably dramatic conclusion about the black hole information. Most of the information remains trapped throughout most of the evaporation process. Effectively, a small black hole behaves as a black hole remnant.

Ram Brustein wrote so far the most recent followup. The author chooses some very conservative language but arguably proposes a much more radical departure from the lore. The event horizon is a wrong concept; it only exists in the classical theory. In the quantum theory, the black hole's Compton wavelength is nonzero which, the author believes, creates a region near the horizon where the densities are inevitably high and quantum gravity is needed to predict what happens in this new extreme region.

I guess that arXiv.org hasn't hit a firewall yet so new and new followups will keep on emerging.

Your humble correspondent has an opinion what happens but I don't want to extend this cacophony. You must already feel it's crazy. There's surely no consensus here at all and if there were any majority, you would manifestly see that it's irrelevant. The researchers don't seem to agree about anything at all! ;-) Some of the papers are potentially compatible with some of the other papers but you won't find a pair of papers that are really answering the question by Polchinski et al. in equivalent ways.

It's plausible that the reason is that all the questions "what an infalling observer sees and feels" is ill-defined. He may feel "nothing special" but the transformation of the quantum information needed to produce his future state may become arbitrarily contrived once he crosses the horizon, with no need to have any simple relation to perceptions by other observers. After all, extremely singular coordinate transformations are bound to translate to extreme transformations on the Hilbert space, especially if it includes some Planckian degrees of freedom (well, degrees of freedom interpreted as "Planckian" by some of the near-horizon observers). Well, one of the papers above was making a similar point. Perceptions and observations depend on the sensory system's being described by a predictable Hilbert space that reacts in predictable ways. If you can't isolate the Hilbert space that behaves as an "ordinary Hilbert space for the sensory system", it makes no sense to talk about someone's perceptions. (I don't really need to reconstruct eyes; what may get destroyed at the event horizon are much more brute pieces of material, too.) On the other hand, when you redefine the degrees of freedom and evolve them by an ad hoc evolution you would expect outside the black hole, it's not a problem and it won't lead to real contradictions with the things outside because the infalling observer is never going to liberate herself, anyway.

I also think it's problematic to assume that the radiation may be described as a pure state even before the black hole evaporates. The state of the radiation may be obtained by tracing over the interior and the horizon degrees of freedom. Even if the strictly internal degrees of freedom are reshuffled outside degrees of freedom, the influence of the near-horizon degrees of freedom could still make the state of the "radiation only" mixed. One may only be sure about the purity when the black hole is really gone.

Well, I actually think that Polchinski et al. and many others are doing exactly the opposite mistake, too. They think that the radiation is maximally entangled with the black hole so it must be described by a heavily mixed state and can't be maximally entangled with someone else. However, the very point of complementarity, as I understand it, is that the black hole interior's degrees of freedom are just "scrambled copies" of the external ones so you shouldn't double count them (which would be spurious quantum xeroxing). The radiation without the interior is nearly or entirely in a pure state at the Page time! I realize this paragraph says exactly the opposite than the previous one but whichever way it goes, I feel they're not being careful about these important considerations.

At any rate, it surely looks bizarre that the quantum gravity folks can't agree about such a seemingly elementary question, namely the existence and character of the hypothetical firewalls. Many of them are excellent folks but maybe they have focused on too ill-defined questions. Maybe this huge cacophony is a warning sign that the research into these "excessively conceptual" questions got stuck in a swampland observed in a letter by Richard Feynman to his wife after he visited the 1962 conference on (general) relativity in Warsaw:

"I am not getting anything out of the meeting. I am learning nothing. Because there are no experiments, this field is not an active one, so few of the best men are doing work in it. The result is that there are hosts of dopes here (126) and it is not good for my blood pressure. Remind me not to come to any more gravity conferences!"

Are we there again? The black hole interior will always be a mostly inaccessible place for most lucky people so these questions will remain theoretical. But are they meaningful as theoretical questions at all? When you look at the amplitudes that string theory allows you to naturally calculate, such as the S-matrix in various Minkowski spaces, you will find out that the "perceptions of an infalling observer" are not among these calculable things. Maybe string theory has a very good reason why it's trying to hide those would-be observables from us! When I wrote about the reincarnation of the infalling observer, it wasn't quite a joke. I really feel that questions about the infalling observer may be somewhat analogous to various spiritual questions about near-death experiences etc. Some of them may be inaccessible to science – and really ill-defined from a scientific viewpoint.