This blog post is here just to promote two new hep-th papers on the black hole interior. Both papers have 4.0-4.5 pages in total and use the same two-column revtex macro of \(\rm\TeX\). The Verlinde brothers wrote

Behind the Horizon in AdS/CFTwhich calls the recent Papadodimas-Raju (PR) construction "elegant" and debunks a potential paradox that could follow from the state dependence of the internal operators by generalizing the PR construction to mixed states with a low enough von Neumann entropy. They seem to say that the detailed mathematical ideas were already contained in their November 2012 paper linking the black hole information puzzle to error correcting codes.

As I said before, I believe that a similar construction must also exist for density matrices of a near-maximal von Neumann entropy as well (they can be visualized as pure entangled states involving two black holes so that the von Neumann entropy of the black hole A becomes the A-B entanglement entropy) but the resulting interior operators one could construct in that case would live in the Einstein-Rosen bridge instead, thus providing us with an explicit constructive proof of the Maldacena-Susskind ER-EPR correspondence.

Verlinde and Verlinde also offer a transparent, PR-based algebraic proof that microstates with a firewall have to be non-equilibrium states and that transformations on the black hole Hilbert space that keep the firewall (or its absence) also keep the definition of all the interior field operators. It looks sensible and it's great, refreshing news to see apparently valid physics signed by these Dutch names again, as opposed to some entropic-gravity-related junk, for example. ;-)

David Berenstein and Eric Dzienkowski offer some argumentation (I don't use the word "argument" because I think that such a word would indicate that I think that it is a valid argument) based on the BFSS Matrix Theory.

Their paper

Numerical Evidence for Firewallsidentifies gapless and "gapful" zones for some fermionic modes with the exterior and the interior of a black hole. Their effective theory based on the simple integrating out of the off-diagonal matrix modes breaks down exactly at (and beneath) the event horizon which they consider to be an argument for the death ("drama" or "firewall") at the event horizon.

In reality, I think that it just shows that the naive method to construct the field operators by the semiclassical ways gets altered at (and beneath) the event horizon, in agreement with what the PR construction says. There's no evidence that there's no life in the interior; it's just evidence that it becomes harder to construct the interior field theory modes in terms of the degrees of freedom available outside the black hole (or at infinity). In this respect, I think that the BFSS Matrix Theory and AdS/CFT work analogously.

## snail feedback (8) :

Dear Lubos,

Since you are talking about black holes again I thought that this would be the place to ask about a topic you talked about a while back with hawking radiation. I am trying to understand what you meant when you said causality was violated. Do you mean general relativity's version of causality is violated where stuff can't travel faster than the speed of light? Or do you mean that black holes can send information into the past and kill it's own grandmother? Or maybe you mean that space is somehow changed so that distance no longer means what it normally means or something? I am sure you have explained it before, but I would also really appreciate a beginners level article about "tunneling" and how it relates to this causality violation.

Thanks for the articles!

Dear Lubos: Has any one suggested possible future experimental evidence from looking at the EM waves emitted when material is falling into black holes in the two cases,firewall or no firewall? Or it is hopeless at this time and one has to rely on theoretical arguments only.

probably it was just a small and excusable glitch of "crackpottery"... :p I ask myself sometimes in what conditions would I stop believing in locality, causality, gauge invariance of observables etc. and I am still not sure what to say... all in all, I am too looking forward for Lubos's answer to this question...

Hi Lubos:

Thanks for pointing to our paper. Our purpose was to show that there is something like a horizon appearing in the matrix model (we need a good reason to excise some part of the geometry). To define a horizon something kind of drastic needs to happen.

We don't know if this is really a firewall, but it acts like one for certain classes of questions.

Dear David, thanks for you visit! Hasn't at least the event horizon always *look like* a singularity where something drastic is happening? It has g_{00}=0, right? And so on. But it was a coordinate singularity. In classical GR, a coordinate transformation undoes it. In QFT, a coordinate transformation has to be promoted to a nonlinear field transformation which is a much harder thing.

So I don't find it surprising that it *looks like* there is something special, and I don't think that this observation implies that an observer will feel anything special while crossing the horizon.

The argumentation and the post says it "looks like" and "certain class of questions" . That Is substituting a pedalogical preferred reference observer for reality, right? Reality does not have any class of questions to prefer or particular probe which can answer them all?

On the other hand Verlinde conclusion : "misguided attempt to capture complete Hilbert space In a single semi-classical space .. ." Which is what I had understood from several of your posts

You say that you think that BFSS and CFT here are analogous, I assert that you do not merely think this but know it and will shortly honor us with the full details. In meantime I shall hopefully not be screwed for thinking that:-)

Hi Lubos:

I agree with your comments on GR, and how that might be related to operations in QFT. Remember that the event horizon is defined globally and has a well defined geometric meaning.

In order to ask about the physics of crossing the horizon (in QFT), we actually need to know where the horizon is in QFT variables. From some conversations I have had with various people, they are not even convinced that one can even speak of a horizon in QFT variables (statements like the QFT can't see inside the black hole from QFT correlators at finite time, etc), so studying the system with probes that look at observables in a different -more local- way is the natural thing to do.

We argued that there is a region that should be excised from the probe moduli space under certain rules (the typical probe D-particle setup). There might be a better way to do it than dumb integration of off-diagonal modes, but I don't know how.

If we look inside that bad region, it is still seen by the QFT variables, and it looks weird (not particularly local).

This needs to be interpreted. In my opinion we had to choose one interpretation: I don't like wishy-washy papers that refuse to take a position when they have some results that are suggestive. Not doing so represents a lack of `courage' (it's a question of whether you believe strongly in your method and are willing to follow it to the ultimate consequences or not).

In this sense, the interpretation might be completely wrong, but the important claim in the paper is that we have a well defined geometric locus that we have argued represents the location of the horizon in QFT variables.

Dear David, thanks for your explanations.

But I think that what you present as an advantage is a part of the flaw of your paper. The horizon shouldn't be "a well-defined locus" at the quantum level. A particular place associated with the horizon is surely just an artifact of the semiclassical approximation, isn't it?

This has become clear in many recent papers that I consider at least approximately right. One can't consistently get the information out of the hole while assuming a particular semiclassical background to be OK for all the microstates.

And the claimed non-existence of the black hole interior isn't just about the breaking of some particular prescription for the degrees of freedom; it is the claim that there's no way to define the interior field modes, something that you haven't demonstrated (and couldn't demonstrate because Raju-Papadodimas, for example, have brought a clear proof that it *is* possible to define them so that all the smoothness, approximate locality, equivalence principle, and unitarity conditions are obeyed).

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