Semiclassical S-matrix for black holes

TL;DR

This paper introduces a semiclassical approach to compute the gravitational S-matrix for black hole formation and evaporation, incorporating back-reaction effects, and demonstrates its effectiveness through toy models with results consistent with black hole entropy.

Contribution

It presents a novel semiclassical method for calculating gravitational S-matrix elements that includes back-reaction, advancing non-perturbative quantum gravity analysis.

Findings

Probability of reflection matches exp(-B), with B as black hole entropy.

Method applies to both neutral and charged shells, accounting for horizon instabilities.

Results support the interpretation of black hole entropy as the number of states.

Abstract

We propose a semiclassical method to calculate S-matrix elements for two-stage gravitational transitions involving matter collapse into a black hole and evaporation of the latter. The method consistently incorporates back-reaction of the collapsing and emitted quanta on the metric. We illustrate the method in several toy models describing spherical self-gravitating shells in asymptotically flat and AdS space-times. We find that electrically neutral shells reflect via the above collapse-evaporation process with probability exp(-B), where B is the Bekenstein-Hawking entropy of the intermediate black hole. This is consistent with interpretation of exp(B) as the number of black hole states. The same expression for the probability is obtained in the case of charged shells if one takes into account instability of the Cauchy horizon of the intermediate Reissner-Nordstrom black hole. Our semiclassical method opens a new systematic approach to the gravitational S-matrix in the non-perturbative regime.