Observing Hawking Radiation from Inside a Black Hole

[nomadreid]

Usually Hawking radiation is treated from the point of view of an observer outside the black hole (by which I mean the event horizon, not the supposed singularity), in which case it is possible (although maybe not convenient) to treat the black hole as not having an interior. However, let us suppose that the black hole has an interior, and that an observer spends the last few moments of her life looking at the Hawking radiation. Now, I don't want to discuss whether or not a particle is falling in or whether a particle is tunneling out. What I am interested in arises from the observation that the point of view of someone outside can be phrased as looking at the black hole from its future. (If I am stumbling already here, then a correction would render the rest of the question irrelevant.) This seems intuitive, since information takes a while to get there. However, could one say that looking at the emission from the inside was like looking at it from the black hole's past? On one side, this would seem to follow from symmetry, but perhaps that is too superficial and this cannot be said. On the other hand, if it can be said, I have a harder time forming an intuitive justification (beyond symmetry) for it. So, my questions are: (a) is this a silly extension, and if not, then (b) can one give an intuitive picture of it, perhaps in the form of information transfer? Thanks.

 

[PeterDonis]

What I am interested in arises from the observation that the point of view of someone outside can be phrased as looking at the black hole from its future. (If I am stumbling already here, then a correction would render the rest of the question irrelevant.)

You are not quite stumbling here, but you are a little further on:

However, could one say that looking at the emission from the inside was like looking at it from the black hole's past?

No. Information still takes time to get to you when you are inside the black hole; so you are seeing events in your past light cone, not events to your future.

 

[nomadreid]

Yes, that makes sense. Although I was actually thinking of looking at the emission from the distant past, before the formation of the black hole.

 

[nomadreid]

That which inspired the question was a remark that the emission could be seen as a solution to Maxwell's equations for the event horizon from the far future and from the distant past (before the creation of the black hole), and using a transformation between the two solutions. I am attempting to get behind this remark, without much success.

 

[PeterDonis]

I am attempting to get behind this remark, without much success.

The remark is describing a fairly advanced application of quantum field theory in curved spacetime. The basic idea is that a quantum field state which is a vacuum in the far past gets transformed by the spacetime curvature of the black hole into a thermal state in the far future. But it takes a considerable background in QFT to be able to follow the details. I first learned about it in Wald's 1993 monograph on QFT in curved spacetime and black hole thermodynamics, which would be an "A" level reference here on PF.

 

[nomadreid]

Thanks, PeterDonis, for the summary and the warning. "For fools rush in where angels fear to tread." Aware of my limitations, I will then leave this topic in the category "maybe in another life I will choose Physics for my university studies".

 

[nomadreid]

By the way, here is the reference to that "remark"
http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/hawking.html