A collection of accepted answers on Physics Exchange paint a seemingly inconsistent picture of Unruh radiation and it's isotropy. One of the most sophisticated answers, from Lubosz Motl, to the question Is Hawking radiation really the same as Unruh radiation states that Unruh radiation is the flat-space limit of Hawking radiation. Explicitly, an observer maintaining a fixed position in Schwarzschild coordinates is necessarily accelerating; that observer experiences Unruh radiation, and if the observer is at infinity, that radiation is interpreted as Hawking radiation.
The answer to Is the Unruh radiation isotropic? suggests that the radiation is coming "from the horizon", and that it could be blocked by a thermal blanket, which seems to contradict the idea that one is sitting in a thermal bath. (That is, the vacuum is "everywhere", so when I accelerate, my guts and muscles should experience Unruh radiation, and not just my skin. It's conventionally said to be isotropic. This is not at all the same as saying that my skin is feeling warmth coming from the direction of the horizon.) Can Hawking radiation be blocked by a thermal blanket (or a lead brick) or is it experienced as a bath? It is conventionally said that a freely falling observer experiences no Unruh radiation. Yet, near a BH, there is still an event horizon for the freely falling observer, and thus the observer would necessarily observe Hawking radiation (but not Unruh radiation). Is that correct? That Hawking radiation is then perceived as a flux from a direction; can it be blocked and shielded against?
The answer to Direction of Unruh radiation invokes the idea of a "Rindler wedge" and states that "Rindler particles (are) without physical direct meaning." I find this confusing: surely if I accelerate and carry a thermometer with me, it will quickly reach thermal equilibrium, and report a non-zero temperature? It is sometimes said that spacetime itself is falling into a black hole (that is certainly the interpretation invited by the Christodolou and Rovelli work at arXiv:1411.2854) and so, in that question, it is imagined that an observer accelerating above the horizon would experience a "headwind" much as a bicyclist might, yet curiously in the form of a thermal bath. Again, this seems to contradict the notion of Hawking radiation coming "from" the event horizon (a "tailwind"). I believe that the correct resolution is that one should not think of Hawking radiation as originating from some thin shell of distance epsilon above the horizon, but rather as momentum eigenstates of indeterminate position: this is why its not directional.
One last: in Why is there a flux of radiation in the Hawking effect but not in the Unruh effect? (and other questions), the answer provided by Lubosz states that "the static observer sitting on a heavy star doesn't see any radiation!" Yet other discussion suggests that an observer riding a rocket near that very same star would perceive Unruh radiation, because there is a horizon that forms due to acceleration. If there's a horizon, then surely it matters not if one is sitting on a chair on the surface of the heavy star, or is riding a rocket just slightly above it: either way, there is a horizon!
Insofar as Hawking radiation is a flux, one could, in principle, ride it on a solar sail, as, after all, I should feel a momentum transfer from it. Which should provide an acceleration. If I deploy my solar sail just above the event horizon, is that flux sufficient to nudge me, err, um, I'm not sure what I'm asking, but, uh, how would that work right at the horizon? Is it no longer a flux, there?
The core confusion appears to have something to with the Bogoliubov transformation, which "feels like it should be" a "local" transformation applied at the (accelerated) space-like tangent space of a manifold. Why does it "feel like that"? Because this tangent space is what provides the coordinate frame for Hamiltonians to be written in: a local symplectic manifold, over there, where one is accelerating, providing the coordinates, and then using those coords to write conventional 2nd-quantized (yet covariant!) QFT in that frame. That all sounds peachy-keen, except that those local coords need to be connected to, or transported to other, distant, inertial frames, in such a way that those field excitations which "fell and disappeared" behind the horizon are no longer present, leaving behind a real particle flux (at the temperature of the horizon), i.e. the Hawking radiation.
So maybe my real question is: is there a recommended review article? One that treats the topic from a geometric view, i.e. showing how to take a Hamiltonian/symplectic frame of reference, in the accelerated frame, and transport/connect the tangent vectors and 1-forms over to an inertial frame, such that those vectors and 1-forms that "fell behind the horizon" are no longer present in the inertial frame? (Maybe I need to work with jets, and not 1-forms, to get it right? some non-commutative thingy on a 2-jet?) Bonus points for doing it on generic pseudo-Riemannian spaces (won't work on Riemannian spaces, because it seems that at least one time dimension is needed) and super-duper bonus points for working with spin structures? (why? Because spin structures are cough cough "where fermions come from", roughly speaking, when one 2nd quantizes them.)