Where from Hawking radiation actually arise? I would like to connect the answer with the technical derivation along the lines of the original calculation by Hawking (a modern account of which is given in Harvy Reall's notes). I have seen this where the three answers apparently don't agree with each other entirely.
i. The first answer points out to tunneling process (whose math I would like to see) or particle-antiparticle production near event horizon none of which isn't directly connected to the original derivation. Well, the particle-antiparticle picture is claimed to be somewhat connected because we can find their mention in many "formal" places (also) including Hawking's original paper. (Somewhere else it is claimed to be wrong/heuristic). In the technical derivation in which step exactly do we utilize this "vacuum turning to particle-antiparticle pair" thing implicitly?
I am actually partially convinced with Ben Crowell's answer that the radiation comes not exactly from the horizon but from a region away from it. But then
a) How do we justify the use of geometrical approximation far from the horizon in Hawking's derivation?
b) In an alternate derivation (for Schwarzschild black hole---not a collapsing spacetime like in Hawking's derivation) detailed in Carroll's book, the author uses Unruh temperature for a static observer and redshift it to infinity to find Hawking temperature; there also the static observer is necessarily near the horizon---otherwise we can't apply the Unruh temperature formula correctly because only the near-horizon geometry of Schwarzschild spacetime is Rindler. These two observation seems to point out the fact that the radiation is necessarily coming from near the Horizon---although the second point seems invalid because accelerated observers do Unruh-radiate in Schwarzschild geometry too.
And how do we know that the particles are not coming from a time when the black hole didn't form? If we look at this diagram (adapted from Harvey's notes) used for backtracing things become more confusing (to me)
Reading this would be like (according to an observer at infinity)---A wavepacket started from past null infinity away from the horizon at a retarded time after which if it had started it would go inside the hole. It went near the horizon before it's formation at very late times and stayed near the horizon for the rest of it's life while coming to us---the observer. It was joined by another wavepacket coming from infinity which started at a later retarded time, hence heading for the event horizon but got scattered towards future null infinity instead. Much of the results of the derivation follows from the change in frequency of the Schwarzschild modes due to extreme blueshifting near the collapsed matter . So apparently the collapsing spacetime(partially Maimon's POV in the linked answer)/some stuff at past null infinity created the Hawking radiation. So how do we prove that these two are not responsible and the event horizon is the culprit of creating Hawking radiation, from this backtracing framework? As mentioned above, there are reasons to believe in event horizon creating the Hawking quanta but I can't understand how that fits within Hawking's original derivation.
This might seem like a duplicate of the linked question but since most of the answerers there are not active members of this community anymore and that many years have passed since the Q/A and (possibly) we have a better picture, I took the risk of reposting essentially the same question but nonetheless with new issues raised.
