How black holes burn: Entanglement entropy evolution for an evaporating black hole

Abstract

We present a calculation of the rate of information release from a Schwarzschild black hole (BH). We have recently extended Hawking's theory of BH evaporation to account for quantum fluctuations of the background geometry, as well as for backreaction and time-dependence effects. Our main result has been a two-point function matrix for the radiation that consists of Hawking's thermal matrix plus off-diagonal corrections that are initially small and become more important as the evaporation proceeds. Here, we show that, if the phases and amplitudes of the radiation matrix are recorded over the lifetime of the BH, then the radiation purifies in a continuous way. It is also shown that our framework achieves a rate of information release from a semiclassical BH that is faster than that predicted by Page on the basis of generic unitarity arguments. When the phases of the radiation matrix are not tracked, we show that it could perhaps purify, but only parametrically close to the end of the BH evaporation. Our main technical tool in the quantitative treatment of this purification is the purity of the radiation matrix and, its inverse, the participation ratio. These can be related to the Renyi entropy of the density matrix of the emitted radiation.