Solvable Models for radiating Black Holes and Area-preserving Diffeomorphisms

TL;DR

This paper introduces a new framework for generating exactly solvable 2D dilaton gravity models, based on area-preserving diffeomorphisms, which can interpolate between known models and extend to spherically symmetric Einstein gravity.

Contribution

A novel method to produce a family of solvable 2D dilaton gravity models via field redefinitions that preserve area and Weyl invariance, extending previous models.

Findings

Mapped original theories into a large family of solvable models

Interpolated between Russo-Susskind-Thorlacius and Bose-Parker-Peleg models

Outlined extension to spherically symmetric Einstein gravity

Abstract

Solvable theories of 2D dilaton gravity can be obtained from a Liouville theory by suitable field redefinitions. In this paper we propose a new framework to generate 2D dilaton gravity models which can also be exactly solved in the semiclassical approximation. Our approach is based on the recently introduced scheme to quantize massless scalar fields coupled to 2D gravity maintaining invariance under area-preserving diffeomorphisms and Weyl transformations. Starting from the CGHS model with the new effective action we reestablish the full diffeomorphism invariance by means of an adequate family of field redefinitions. The original theory is therefore mapped into a large family of solvable models. We focus our analysis on the one-parameter class of models interpolating between the Russo-Susskind-Thorlacius model and the Bose-Parker-Peleg model. Finally we shall briefly indicate how can we extend our approach to spherically symmetric Einstein gravity coupled to 2D conformal matter.