Evaporating BH and infalling observers - I am puzzed

A calculation like this is probably based on semiclassical quantum gravity, in which case the results would be open to question since we don't have a complete theory of quantum gravity and thus wouldn't know if the approximations are good (and having just read https://www.amazon.com/Black-Hole-War-Stephen-Mechanics/dp/0316016403 I think a lot of physicists in quantum gravity would dispute the conclusion that an infalling observer doesn't reach the horizon before it evaporates)...anyway, if this is a question that touches on quantum gravity issues, maybe it should be in the "Beyond the Standard Model" forum?

 

Here another post on the Vachaspati, Stojkovic, Krauss paper,

https://www.physicsforums.com/showthread.php?p=1534827#post1534827.

Wikipedia is wrong. In particular,

is wrong.

The (absolute) [edit]event horizon[/edit] is a particular set of spacetime events, and, for an infalling observer, one of the events on the event horizon is also an event on the observer's worldline.

 

Exactly.

 

But this isn't the event horizon of the black hole.

 

From the Wikipedia article,

 

perhaps, i am simply too dim, but i find hawking's technical writing to be completely incomprehensible. his chapters in "The Nature of Space and Time" are so confoundingly obtuse, i get lost within a few paragraphs, whereas the chapters by Penrose are succint, clear, and meaningful. It makes me wonder about hawking - it reminds me of feynman's comment that "if you are not able to express an idea clearly to a layperson, you dont understand it well enough yourself..." (not a direct quote)

i have much more confidence in the works of MTW and Wald.

 

What do you mean by "HIS" horizon? The event horizon of a black hole is an objective thing, it isn't frame-dependent...it refers to the boundary of the region where it becomes impossible for light to escape. Of course, there is nothing about this definition that would suggest an infalling observer would notice anything weird or different at the moment they crossed the horizon, the definition just says that if the observer sets off a spherical flash of light before crossing the horizon some of the light will eventually get far away from the black hole, while if the observer sets off a flash inside the horizon all of the light will eventually hit the singularity (at least in the case of a nonrotating black hole, for a rotating black hole some trajectories avoid the singularity even though they never get back to the original region of spacetime they came from outside the horizon). But at the moment the observer sets off the flash it looks just the same to him regardless of whether he's inside the horizon or outside.

 

It looks like the definition of the "apparent horizon" of a black hole is given on p. 320 of Hawking and Ellis' The Large Scale Structure of Space-Time, it's the "outer boundary of a connected component of the trapped region", with the "trapped region" defined at the top of the page--when you say this is frame-dependent, do you mean to suggest that the set of events in spacetime that lie on the apparent horizon would depend on your choice of coordinate system?

Also, why are you interested in the apparent horizon rather than the absolute horizon? When physicists discuss the event horizon of a black hole they are more often talking about the latter I think, and I'd bet the quote from the paper in your OP about there being "no event horizon to cross" probably was too unless they said otherwise (or unless someone here can follow enough of the math to know for sure).

By the way, on the subject of what actually happens to observers and light falling into evaporating black holes, this paper shows some different proposed Penrose-Carter diagrams for evaporating black holes that correspond to different theories about this. And on the subject of different definitions of the horizon, here is a review paper comparing and contrasting various definitions (along with a discussion of the conservation of energy problem in GR), and this paper talks about some new ways of defining it that are more local than previous definitions. Finally, here is a good paper on the classical theory of black holes, and here is one on the current state of the astrophysical evidence for them.

 

In another thread, Event horizon - physical or chart-dependent?, I raised a question about apparent horizons and got answers which only partly addressed my concerns.

 

Wiki states that the apparent horizon is inside the absolute horizon (EH) but when looking at the tortoise coordinate (r*) in Eddington-Finkelstein coordinates, I'm almost under the impression that the apparent horizon is outside the EH, synonymous in some way with v=t+r*=0 for ingoing radial null coordinates, sometimes referred to as 'the surface of last influence'-

http://www.sron.nl/~jheise/lectures/kruskal.pdf" [Broken] (page 66)

'..Figure 8.9 Surface of last influence. Spherical gravitational collapse is shown here in ingoing E-F coordinates. For each external particle or external observer there is a moment of the ”birth of the black hole”. The set of such moments form the ”surface of last influence”. Before passing this surface external observers can in principle still shine a flashlight onto the contracting star and receive the bounced light or he can collect a few baryons from the surface. After passing surface of last influence observers cannot interact (matter cannot be influenced) and can consider the object a black hole..'

the above implies there are trapped surfaces between the surface of last influence and the event horizon, possibly giving rise to an apparent horizon.

 

Kip Thorne's book Black Holes and Time Warps has a diagram on p. 418 of both the absolute and apparent horizon in the case of a black hole that grows because it swallows some additional matter, he definitely shows the apparent horizon as being inside the absolute horizon during the period when the two horizons disagree. What makes you think the apparent horizon, defined in terms of "trapped surfaces", has anything to do with the concept of the "surface of last influence"? I don't really understand the technical definition of a "trapped surface" in GR so I'm not saying you're definitely wrong, just that you don't really explain your reasoning for equating the two.

Why do you think the quote implies that? The quote doesn't even mention the notion of trapped surfaces...

 

If Black Holes and Time warps shows the apparent horizon inside the absolute horizon then that's pretty conclusive but I'll shed some light on why I thought the apparent horizon had anything to do with the surface of last influence.

I initially thought that the quote I provided was in some way describing this effect from wiki-

'..An apparent horizon is a surface defined in general relativity as the boundary between light rays which are directed outwards and moving outwards, and those which are directed outwards but moving inwards..' I now realise that's not the case.

In mass inflation, there is the mass-energy of the radiation influx (δm) which is associated with the inverse power law decrease of late-time fields, (sometimes referred to as Price's power law damping of radiative tails) which are radiated then backscattered into the BH at the potential barrier (http://arxiv.org/PS_cache/gr-qc/pdf/9411/9411050v1.pdf" [Broken], page 2, last para) the potential barrier appearing synonymous with the surface of last influence, giving the impression that this information, while outside the event horizon, is 'trapped'.

Also, the surface of last influence is also synonymous with the ingoing null coordinates (v) becoming negative. On that note, in the case of v=t+r*, what units are used for t? In http://www.phys.ufl.edu/~det/6607/public_html/grNotesMetrics.pdf" [Broken], (page 10) time seems to be counting down from infinity to zero, parallel (if not exactly) with the coordinate radius.

Source where r₀ appears to be the surface of last influence-
http://www.damtp.cam.ac.uk/user/sg452/black.pdf [Broken] diagrams page 8-9

r₀ as the potential barrier-
http://relativity.livingreviews.org/open?pubNo=lrr-1999-2&key=Chandra83 [Broken] eq 30

Would it at least be reasonable to say that the surface of last influence and the potential barrier are the same thing?

 

I now get it that the surface of last influence is a temporary phase that exists just as a star collapses into a black hole, anything on the inside of the surface of last influence as the black hole forms, regardless of its velocity, will be dragged into the black hole, the surface of last influence eventually becoming the event horizon (http://www.sron.nl/~jheise/lectures/kruskal.pdf" [Broken] where BH radial perturbation equations are similar to equations used in QM.