Firewalls, smoke and mirrors

Abstract

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 $N_{coh}$ 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 $N_{coh}^2$ in Schwarzschild units. So, if $N_{coh}$ is parameterically larger than the square root of the BH entropy $S_{BH}^ {1/2}$, 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 $S_{BH}^{1/2}$, 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 $N_{coh}=S_{BH}^{1/2}$ 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 $N_{coh}$. When the rate of information release becomes order unity, the semiclassical approximation starts to break down and the BH becomes a perfect reflecting information mirror.