[EDITED] I'm a postdoc working in cond-mat/quant theory, and I've heard some explanations of Hawking radiation that strike me as inconsistent or silly (e.g., in terms of pair production). I'm hoping someone can confirm that my concerns below don't apply to the rigorous derivation of Hawking radiation. I'm also fine with QFT / technical details, and I've obviously read Wiki lol.
Apologies for the lengthy question, and a huge thank you to anyone who takes the time to respond!
I have been assured since posting my original question that the pair-production picture is cartoony and I need not worry about it. Thanks for that, and I'll skip ahead to other derivations.
To add to the original version, my real question pertains to why should we expect to see Hawking radiation? Basically, if the derivation comes from the Unruh effect, then I would like to know why the experience of an accelerating observer is relevant to our experience. After all, aren't we inertial with respect to any black hole (i.e., our solar system follows its geodesic)? Or in Hawking's derivation, in what sense does what happens in two extreme stationary limits have any bearing on what we experience at intermediate times? Note that I could easily be missing details about the intricacies of doing QFT on curved space time.
I'm told that one explanation derives from the Unruh effect. As I recall, what an inertial observer perceives as the QFT vacuum will appear otherwise to an accelerating observer, who will observe lots of excitations (perhaps of a different QFT). While the vacuum state is certainly in thermal equilibrium at $T=0$, I don't see why the noninertial observer perceives the system as being in thermal equilibrium at temperature $T>0$ (as opposed to out of equilibrium)? Additionally, assuming thermal equilibrium, I am curious as to the precise argument that the noninertial observer perceives "radiation"?
More importantly still, I fail to see what this has to do with inertial physics. We learn very early on that the physics of inertial frames need not apply in noninertial frames (and vice versa). Clearly, an inertial observer (who perceives the $T=0$ QFT vacuum) cannot perceive the Unruh radiation experienced by a noninertial observer (who experiences a $T>0$ thermal bath). Moreover, I have seen several papers disputing the existence of Unruh radiation. So it is not clear to me where the Unruh effect should enter into the derivation of Hawking radiation.
Basically, I'm confused as to how the required noninertial frame comes into play. After all, while "free fall" under gravity appears to us as acceleration, in GR, this results from how matter modifies the embedding of 3+1D spacetime in itself. There is a choice of frame in which "free fall" is simply inertial, geodesic motion, no? I'm going to ignore the fact that gravity often leads to rotating orbits...I don't know if this is important or not, but will assume it is inconsequential for the simplest cases.
Naïvely I would think our solar system is in an inertial frame, following geodesics in the same way an object in free fall does. To me this seems to imply that, from the perspective of GR, any observer accelerating under gravity alone is in the same inertial frame as all others, and should agree on physics. I also assume that what we identify as the QFT vacuum is defined in this same frame (where we live and eat). So I don't see how the Unruh effect applies.
That is, unless one identifies an accelerating observer—e.g., one falling toward the event horizon who accelerates away to forestall their own demise. However, that observer would cease to be in the same inertial frame as the rest of us (and where the QFT vacuum lives). While they would experience the Unruh effect, the physics they observe would not be relevant our own perception. Any "test particle" we use to probe physics near the event horizon should be in an inertial frame relative us, right? Basically, no conclusion of an accelerating observer has bearing on inertial physics.
Hopefully I've clearly explained my own confusion; if not, I'm happy to clarify!
[UPDATE] Thanks to your answers I am now aware of a much better derivation, which is on much stronger footing and makes physical sense. Thanks also for the references, I plan to read through these!