Black Hole Fire Walls, Brick Walls, and the Casimir Effect

[.Scott]

TL;DR Summary

I cite a few articles that have demonstrated to me that my former view of Black Hole event horizons was critically incomplete - and that the BH EV is as much about QM as it is relativity.

At the heart of this posting is the questions raised in this Nature article on the nature of death for BH visitors. (I'll call that visitor "Alice".)
Physics is still struggling with this question - and so am I.

Until recently, I was very impressed with the Equivalence Principle which confers no special status to the local effects of a Black Hole's event horizon. In that sense, I very much subscribed to Jocabson's and Bousso's sentiments as quoted in that Nature article:

“It was outrageous to claim that giving up Einstein’s equivalence principle is the best option,” says Jacobson. Bousso agrees, adding: “A firewall simply can’t appear in empty space, any more than a brick wall can suddenly appear in an empty field and smack you in the face.” If Einstein’s theory doesn’t apply at the event horizon, cosmologists would have to question whether it fully applies anywhere.

I was also willing to give wide license to Alice's experience once she crossed the horizon - since any message she had for the outside world would be severely scrambled, delayed, and converted to Hawking's Radiation before received by any of us "outsiders".

But an issue I had with the Bekenstein Bound (described here) has pulled me in to further reading. The problem is that whatever happens to Alice should still conform to Physics, and by my naïve thinking the instant she reaches the event horizon, she needs to either speed past mass, stop her decent, or add information to a region just below the event horizon that was already at its Bekenstein capacity. Perhaps the worse part of my problem was that this sudden transition could not possibly be sudden - because there was nothing that I knew about that "suddenly" changed at that EH - at least not with regards to local gravity.

So I went looking for articles that might suggest any kind of mass inventory issues or trajectory-altering issues near a BH event horizon. And here's what I've found so far:

First, there's been a bit of an update to the Bekenstein Bound called “generalized” covariant entropy bound (GCEB) as described by Raphael Bousso and behind a paywall here (unread by unpaid me).
In terms of addressing my concerns, GCEB doesn't directly help. In fact it closes loop holes that I had not fully considered.

Next, there is this section in the Bekenstein wiki article titled "Proof in Quantum Field Theory".
I apologize for the reference to a section in a wiki article - but that section does provide a good description of an interesting concept.
It cites two references to supporting articles:
"Relative entropy and the Bekenstein bound" by Casini which lays out the basic math; and
"Bound states and the Bekenstein bound" by Bousso which provides a tie-in to the Casimir effect.
The concept is that Hawking radiation can be explained, in part, by Casimir-based negative energy being sucked towards and past the event horizon.
From what I can tell, these effects would occur in the neighborhood of the event horizon, change the Bekenstein Bound information tally, and seem to address my "suddenness" issue by extending the effects to a zone above the EH. Also, since it is very much tied to the non-gravitational characteristics of a Black Hole, it addresses Bousso's (and my) discomfort with a "brick wall appearing in an empty field".

Finally, no sooner do I accommodate myself to the possibility of a brick wall, that I find that
a Nobel Laureate (Gerard 't Hooft) has built one. Since I haven't found a direct link authored by him, I will cite sources that use his work. This may actually be better, since I don't have to do any analysis myself.
Under the category of "BH atmosphere", :
"Why the entropy of spacetime is independent of species of particles: the species problem"
This article works with a "scheme" is based on Hooft's Brick Wall BH Event Horizon model and is described in the article's Abstract:

The Hawking radiation emits all species of particles, but the Bekenstein–Hawking entropy is independent of the number of the species of particles. This is the so-called species problem—a puzzling problem for a long time. In this paper, we suggest a solution to this problem. A result of the scheme is that the black hole atmosphere has a mass equaling 3/8 mass of a classical Schwarzschild black hole, which agrees with ’t Hooft’s brick wall model.

From what I read, this "Brick Wall" scheme is pure pragmatics. It's based much more on "this is what needs to happen" than "these are the mechanics that would make this happen".
That article makes this statement:

The atmosphere accounts for 3/11 of the mass of a Schwarzschild black hole.

To me, this looks very promising. Alice needs to deal with a "Brick Wall", a kind of gate keeper before she reaches the event horizon.
Since the mechanics have yet to be worked out - I have every reason to hope that some version of these bricks can occur throughout the entire volume of the BH.

 

[PeterDonis]

I cite a few articles that have demonstrated to me that my former view of Black Hole event horizons was critically incomplete - and that the BH EV is as much about QM as it is relativity.

One key point to remember: everything in these articles is speculation. We do not have a good theory of quantum gravity, and we have no experimental evidence in the regime being discussed. All we have is theoretical speculations based on heuristic, intuitive guesses.

 

[PeterDonis]

by my naïve thinking the instant she reaches the event horizon, she needs to either speed past mass

I don't know what this means.

stop her decent

She can't if she's at the horizon. She can only do so if she's above the horizon.

or add information to a region just below the event horizon that was already at its Bekenstein capacity.

This is not correct according to the best current models we have (as opposed to speculations going beyond those models). What those models do say is that the object falling into the hole increases its mass and its horizon area, in such a way that the resulting hole still obeys the Bekenstein bound.

In the previous thread of yours you referenced, you were trying to apply the Bekenstein bound to individual "regions" inside the black hole. But, as I pointed out in my responses in that thread, we have no way of doing this with our current knowledge, since we have no accepted model of a black hole that "builds" it from internal constituents to which the bound could be independently applied.

 

[PeterDonis]

The concept is that Hawking radiation can be explained, in part, by Casimir-based negative energy being sucked towards and past the event horizon.

This is a heuristic model that has a lot of flaws and should not be relied on for general reasoning. We have had a number of previous threads on this.

Note, however, that, at least in the second paper you cite in this connection (the Bousso one), the "Casimir energy" does not appear to me on a quick reading to be used specifically in connection with the above heuristic description of Hawking radiation, but more generally in connection with a known property of quantum fields, that certain quantum field configurations can violate what are called "energy conditions" that are used in a number of critical theorems in classical GR. Bousso is basically saying that these violations also create issues for the usual calculation of the Bekenstein bound. I'll need to read the paper in more detail before commenting further on the specifics.

 

[PeterDonis]

From what I read, this "Brick Wall" scheme is pure pragmatics. It's based much more on "this is what needs to happen" than "these are the mechanics that would make this happen".

I would agree with this comment. I would further point out that the idea of an "atmosphere" just outside a black hole's horizon is not a new one; it has been around for at least a few decades (a layman's description of it appears in Kip Thorne's 1993 book Black Holes and Time Warps). And the general opinion about it is that this "atmosphere" is only detectable by observers who are not free-falling into the hole, like Alice, but are "hovering" just above it, and have therefore a huge proper acceleration. The "atmosphere" then can be understood as similar to Unruh radiation, which is observed by accelerated observers in flat spacetime.

In other words, in QFT in curved spacetime, the very notion of "vacuum state" (or "number of particles present", if you like) becomes observer-dependent. To Alice, free-falling into a black hole, the hole is vacuum and she observes nothing as she falls through the horizon. But to Bob, hovering in his rocket just outside the horizon, there is a hot atmosphere of particles that he can observe. The same underlying quantum field state produces both observations.

On a quick reading, I don't see this point addressed at all in the "brick wall" papers. But I'll read them in more detail before commenting further.

 

[.Scott]

This is not correct according to the best current models we have (as opposed to speculations going beyond those models). What those models do say is that the object falling into the hole increases its mass and its horizon area, in such a way that the resulting hole still obeys the Bekenstein bound.

That sounds good. But with an increase in the horizontal area, would there still be tidal forces?
Edit: I suppose not typical tidal forces - but still spaghettification. But why would there be a collision with anything?

In the previous thread of yours you referenced, you were trying to apply the Bekenstein bound to individual "regions" inside the black hole. But, as I pointed out in my responses in that thread, we have no way of doing this with our current knowledge, since we have no accepted model of a black hole that "builds" it from internal constituents to which the bound could be independently applied.

What was not addressed in that other thread was the "suddenness". If Alice can cross the EV without immediately noticing anything abruptly different, then whatever the gravity-based mechanism that is preserving the horizontal area needs to blend in with her descent. Since that mechanism needs to be in full effect at EV crossing, there should be evidence of it before she reaches the EH.

Do current models deal with that?

 

[PeterDonis]

with an increase in the horizontal area, would there still be tidal forces?

The area of the hole is not "horizontal". The horizon is a 2-sphere, not a plane. The tidal forces at the horizon would be very slightly smaller because the mass of the hole has become very slightly larger.

If Alice can cross the EV without immediately noticing anything abruptly different, then whatever the gravity-based mechanism that is preserving the horizontal area needs to blend in with her descent.

There is no "gravity-based mechanism". The hole's event horizon is not a local concept; it's a global concept. (This is another thing that the papers don't seem to really acknowledge.) So there's nothing locally that needs to happen to make the horizon area slightly larger.

To put it another way, the event horizon is a globally defined causal boundary in the spacetime. Since spacetime includes time, "globally defined" means you can only know exactly where the horizon is if you know the entire future history of the spacetime. Then you can go back and compute where the horizon is. But there is no local way to do the computation.

Some papers, when they use the term "horizon", actually mean a trapping horizon (in more technical language, a marginally outer trapped surface or MOTS), which is a 2-sphere on which radially outgoing light rays do not move outward, but remain on the same 2-sphere with the same area. In an idealized stationary black hole in classical GR, the event horizon is also a trapping horizon, but that is no longer the case for non-stationary holes, i.e., holes that can accrete matter or that can emit Hawking radiation.

A trapping horizon is in principle locally detectable, and at least one paper I have seen (on Bardeen black holes--we have had some previous threads on this which I would recommend looking up) proposes that, heuristically, when quantum fields detect locally that a trapping horizon has formed, their gravitational behavior changes in such a way that it prevents further gravitational collapse (in more technical language, the effective stress-energy tensor becomes like dark energy, which, heuristically, makes gravity repulsive instead of attractive). Such objects could look from the outside like standard black holes, but would have no singularity at the center and no true event horizon since one could still in principle send light signals out to infinity from anywhere inside them (though from deep inside them the light signals might take $10^{70}$ years or more, a typical Hawking evaporation time, to emerge).