Consider three observers in different states of motion relative to a black hole:
Observer A is far away from the black hole and stationary relative to it;
Observer B is suspended some distance above the event horizon on a rope, so that her position remains constant with respect to the horizon;
Observer C is the same distance from the horizon as B (from the perspective of A), but is freefalling into it.
All of these observers should observe Hawking radiation in some form. I am interested in how the spectra and intensity of the three observations relate to one another.
My previous understanding (which might be wrong, because I don't know how to do the calculation) was that if you calculate the radiation that B observes, and then calculate how much it would be red shifted as it leaves the gravity well, you arrive at the spectrum and intensity of the Hawking radiation observed by A. I want to understand how the radiation experienced by C relates to that observed by the other two.
The radiation fields observed by B and C are presumably different. B is being accelerated by the tension in the rope, and is thus subject to something like the Unruh effect. C is in freefall and therefore shouldn't observe Unruh photons - but from C's point of view there is still a horizon ahead, so presumably she should still be able to detect Hawking radiation emanating from it. So I would guess that C observes thermal radiation at a lower intensity than B, and probably also at a lower temperature (but I'm not so sure about that).
So my question is, am I correct in my understanding of how A and B's spectra relate to one another, and has anyone done (or would anyone be willing to do) the calculation that would tell us what C observes? References to papers that discuss this would be particularly helpful.