Quote by genneth
I know... but that transform is nontrivial! E.g. the part of the world line of the infalling observer which is inside the horizon is not even in the spacetime of the asymptotic observer, so the transform must have some singularities; my question is whether they are physical. Searching for literature on this gives remarkably thin results (i.e. none). I really would like to know the answer, but I don't think anyone has it  I would be happy to be shown otherwise.

This is why I don't believe in black holes. To make hawking radiation compatible to an asymptotic observer, an infalling observer would receive an infinitely strong blast of radiation when crossing the horizon. This is why I think the fuzzball is better than the LQG solution, at least how it is interpreted. The infinite blast should be actually the leaking gas of hot sphere made by whatever entity a fundamental theory of quantum gravity regards as fundamental.
EDIT.: Just noticed what suprised said above. So, what I mean is a killer fuzball.