The radiation emitted by a black hole (BH) during its evaporation has to have some degree of quantum coherence to accommodate a unitary time evolution. We parametrize the degree of coherence by the number of coherently emitted particles Ncoh and show that it is severely constrained by the equivalence principle. We discuss, in this context, the fate of a shell of matter that falls into a Schwarzschild BH. Two points of view are considered: that of a stationary external observer and that of the shell itself. From the perspective of the shell, the near-horizon region has an energy density proportional to Ncoh2 in Schwarzschild units. So, if Ncoh is parametrically larger than the square root of the BH entropy SBH1/2, a firewall or more generally a "wall of smoke" forms and the equivalence principle is violated while the BH is still semiclassical. To have a degree of coherence that is parametrically smaller than SBH1/2, one has to introduce a new sub-Planckian gravitational length scale, which likely also violates the equivalence principle. And so our previously proposed model which has Ncoh=SBH1/2 is singled out. From the external-observer perspective, we find that the time it takes for the information about the state of the shell to get re-emitted from the BH is inversely proportional to Ncoh. When the rate of information release becomes of order unity, the semiclassical approximation starts to break down and the BH becomes a perfect reflecting information mirror.
|Journal||Physical Review D - Particles, Fields, Gravitation and Cosmology|
|State||Published - 16 Jul 2014|