Failure of mean-field approximation in weakly coupled dilaton gravity

¹ Institute for Nuclear Research of the Russian Academy of Sciences, 60th October Anniversary Prospect, 7a, 117312 Moscow, Russia
² Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudny 141700, Moscow Region, Russia

^* e-mail: fitkevich@phystech.edu

Published online: 31 October 2018

Abstract

We investigate black hole evaporation in a weakly coupled model of two-dimensional dilaton gravity paying a particular attention to the validity of the semiclassical mean-field approximation. Our model is obtained by adding a reflecting boundary to the celebrated RST model describing N gravitating massless scalar fields to one-loop level. The boundary cuts off the region of strong coupling. Although our model is explicitly weakly coupled, we find that the mean field approximation inevitably fails at the end of black hole evaporation. We propose an alternative semiclassical method aiming at direct calculation of S-matrix elements and illustrate it in a simple shell model.