Do black hole firewalls have observable consequences?

In a paper out last week Niayesh Afshordi and Yasaman Yazdi from Perimeter Institute study the possibility that black hole firewalls can be observed by their neutrino emission:

Firewall Phenomenology with Astrophysical Neutrinos
Niayesh Afshordi, Yasaman K. Yazdi
arXiv:1502.01023 [astro-ph.HE]

In their work, the authors assume that black holes are not black, but emit particles from some surface close by the black hole horizon. They look at the flux of particles that we should receive on Earth from this surface. They argue that highly energetic neutrinos, which have been detected recently but whose origin is presently unknown, might have originated at the black hole firewall.

The authors explain that from all possible particles that might be produced in such a black hole firewall, neutrinos are most likely to be measured on Earth, because the neutrinos interact only very weakly and have the best chances to escape from a hot and messy environment. In this sense their firewall has consequences different from what a hard surface would have, which is important because a hard surface rather than an event horizon has previously been ruled out. The authors make an ansatz for two different spectra of the neutrino emission, a power-law and a black-body law. They then use the distribution of black holes to arrive at an estimate for the neutrino flux on Earth.

Some experiments have recently measured neutrinos with very high energies. The origin of these highly energetic neutrinos is very difficult to explain from known astrophysical sources. It is presently not clear how they are produced. Afshordi and Yazdi suggest that these highly energetic neutrinos might come from the black hole firewalls if these have a suitable power-law spectrum.

It is a nice paper that tries to make contact between black hole thermodynamics and observation. This contact has so far only been made for primordial (light) black holes, but these have never been found. Afshordi and Yazdi instead look at massive and solar-mass black holes.

The idea of a black hole firewall goes back to a 2012 paper by Almheiri, Marolf, Polchinski, and Sully, hereafter referred to as AMPS. AMPS pointed out in their paper that what had become the most popular solution attempt to the black hole information loss problem is in fact internally inconsistent. They showed that four assumptions about black hole evaporation that were by many people believed to all be realized in nature could not simultaneously be true. These four assumptions are:

1. Black hole evaporation does not destroy information.
2. Black hole entropy counts microstates of the black hole.
3. Quantum field theory is not significantly affected until close to the horizon.
4. An infalling observer who crosses the horizon (when the black hole mass is still large) does not notice anything unusual.

The last assumption is basically the equivalence principle: An observer in a gravitational field cannot locally tell the difference to acceleration in flat space. A freely falling observer is not accelerated (by definition) and thus shouldn’t see anything. Assumption three is a quite weak version of knowing that quantum gravitational effects can’t just pop up anywhere in space that is almost flat. Assumption 3 and 4 are general expectations that don’t have much to do with the details of the attempted solution to the black hole information loss problem. The first two assumptions are what describe the specific scenario that supposedly solves the information loss problem. You may or may not buy into these.

These four assumptions are often assigned to black hole complementarity specifically, but that is mostly because the Susskind, Thorlacius, Uglum paper nicely happened to state these assumptions explicitly. The four assumptions are more importantly also believed to hold in string theory generally, which supposedly solves the black hole information loss problem via the gauge-gravity duality. Unfortunately, most articles in the popular science media have portrayed all these assumptions as known to be true, but this isn’t so. They are supported by string theory, so the contradiction is a conundrum primarily for everybody who believed that string theory solved the black hole information loss problem. If you do not, for example, commit to the strong interpretation of the Bekenstein-Hawking entropy (assumption 2), which is generally the case for all remnant scenarios, then you have no problem to begin with.

Now since AMPS have shown that the four assumptions are inconsistent, at least one of them has to be given up, and all the literature following their paper discussed back and forth which one should be given up. If you give up the equivalence principle, then you get the “firewall” that roasts the infalling observer. Clearly, that should be the last resort, since General Relativity is based on the equivalence principle. Giving up any of the other assumptions is more reasonable. Already for this reason, using the AMPS argument to draw the conclusion that black holes must be surrounded by a firewall is totally nutty.

As for my personal solution to the conundrum, I have simply shown that the four assumptions aren’t actually mutually incompatible. What makes them incompatible is a fifth assumption that isn’t explicitly stated in the above list, but enters later in the AMPS argument. Yes, I suffer from a severe case of chronic disagreeability, and I’m working hard on my delusions de grandeur, but this story shall be told another time.

The paper by Afshordi and Yazdi doesn’t make any use whatsoever of the AMPS calculation. They just assume that there is something emitting something close by the black hole horizon, and then they basically address the question what that something must do to explain the excess neutrino flux at high energies. This scenario has very little to do with the AMPS argument. In the AMPS paper the outgoing state is Hawking radiation, with suitable subtle entanglements so that it is pure and evolution unitary. The average energy of the emitted particles that is seen by the far away observer (us) is still zilch for large black holes. It is in fact typically below the background temperature of the cosmic microwave background, so the black holes won’t even evaporate until the universe has cooled some more (in some hundred billion years or so). It is only the infalling observer who notices something strange is going on if you drop assumption 4, which, I remind you, is already nutty.

So what is the merit of the paper?

Upon inquiry, Niayesh explained that the motivation for studying the emission of a possible black hole firewall in more general terms goes back to an earlier paper that he co-authored, arXiv:1212.4176. In this paper they argue (as so many before) that black holes are not the endstate of black hole collapse, but that instead spacetime ends already before the horizon (if you want to be nutty, be bold at least). This idea has some similarities with the fuzzball idea.

I am generally unenthusiastic about such solutions because I like black holes, and I don’t believe in anything that’s supposed to stabilize collapsing matter at small curvature. So I am not very convinced by their motivation. Their powerlaw ansatz is clearly constructed to explain a piece of data that currently wants explanation. To me their idea makes more sense when read backwards: Suppose the mysterious highly energetic neutrinos come from the vicinity of black holes. Given that we know the distribution of the black holes, what is the spectrum by which the neutrinos should have been emitted?

In summary: The paper doesn’t really have much to do with the black hole firewall, but it deals instead with an alternative end state of black hole collapse and asks for its observational consequences. The good thing about their paper is that they are making contact to observation, which is rare in an area plagued by lack of phenomenology, so I appreciate the intent. It would take more than a few neutrinos though to convince me that black holes don’t have a horizon.