Quantum fluctuating geometries and the information paradox II

Abstract

In a previous paper we discussed corrections to Hawking radiation from a collapsing shell due to quantum fluctuations of the shell and the resulting horizon. For the computation of the quantum corrections we used several approximations. In this paper we take into account effects that were neglected in the previous one. We find important corrections including non-thermal contributions to the radiation at high frequencies and a frequency dependent time scale at which the emission of thermal radiation of frequency ω cuts off. Such scale tends to infinity in the limit of a classical shell. The fact that one has almost from the outset non-thermal radiation has significant implications for the information paradox. In particular the amount of non-thermality is considerably larger than what we had estimated before. A naive estimate of the evaporation time leads to a much faster evaporation than in the usual Hawking analysis. arXiv:1908.04270v1 [gr-qc]

Hawking radiation from an evaporating black hole via Bogoliubov transformations

“…The second contribution (20) to the integral does not know about the collapse and falls rapidly with n away from u n = v s2 . To see this we can use the freedom in the definition of u to choose u n − v s2 = 2nπ and the change of variable y = (v − v s2 ) /2.…”

“…In previous works [19,20] we have proposed an introduction of quantum gravity correction to the Hawking radiation of a collapsing system considering fluctuation of the horizon, but the possible extension of the technique to scenarios with evaporation require the description of the Hawking radiation in term of Bogoliubov transformations.…”

An exact, coordinate independent classical firewall transformation

“…A common simplified model is a spherically symmetric distribution of matter collapsing or expanding in a Schwarzschild black hole background, e.g. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. For example, quantization procedures for a single shell collapse demonstrate completely unitary evolution as the shell collapses and subsequently bounces back outwards after a long black-hole-like epoch [10,11].…”

“…Shell models have also been used as geometrical backgrounds to Hawking radiation. In [16,17] the shells were used to refine the description of Hawking radiation to include the changing mass of the black hole, and in [18,19] there is theoretical evidence that at least some quantum information about an ingoing shell crossing the event horizon is recoverable from Hawking radiation, which may help solve the black hole information paradox.…”

“…The theory has gained some traction in the search for black hole microstates [29][30][31][32][33] and is conceptually similar to Hawking radiation models developed on quantum shell backgrounds, e.g. [18,19]. The essence of the firewall transformation can be formulated as an invertible change in basis between the quantum observables for the ingoing and outgoing particles [25]:…”