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- 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:

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:

That article makes this statement:

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.

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:

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".“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.

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:

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".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.

That article makes this statement:

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

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.