As I understand, Hawking radiation leads to black hole evaporation, resp. a black hole would lose mass due to that effect.
Now Hawking radiation is very similar to Unruh radiation, i.e. some (apparent) horizon leads to a thermal bath:
- An inertial observer in Minkowski space does not see radiation.
- A Rindler observer sees Unruh radiation.
- A free falling observer does not observe Hawking radiation from a black hole.
- An observer hovering somewhere over the event horizon of a black hole does see Hawking radiation.
Hence in either case, the inertial observer (1.) sees no radiation whilst the accelerated observer (2.) sees thermal radiation.
Of course, the case U.2 is stationary, i.e. for a Rindler observer the spacetime does not change and the Rindler horizon does not disappear, evaporate or change its distance due to Unruh radiation.
Doesn't this also apply to H.2, i.e. there is just some thermal bath due to acceleration (or due to some horizon), and the black hole does not change in mass?
Moreover, if the black hole did evaporate due to Hawking radiation, wouldn't that lead to conflicting observations from a free falling observer (black hole does not evaporate because no loss of energy / mass because no radiation is emitted) vs. hovering observer (black hole does evaporate because it loses mass / energy due to Hawking radiation)?
Hawking's derivation predicts named radiation, but does that derivation also show that the black hole's mass is changing?