Quantum Black Holes in Two Dimensions

TL;DR

This paper explores quantum dilaton-gravity actions in two dimensions, revealing a Liouville-like structure that avoids certain singularities and analyzing Hawking radiation with back reaction effects, showing a constant emission rate.

Contribution

It introduces a class of quantum actions for dilaton-gravity that are Liouville-like and free of field space singularities, providing new insights into quantum black hole behavior.

Findings

Certain quantum dilaton-gravity models lack field space singularities.

Back reaction effects do not alter the asymptotic constancy of Hawking radiation.

Quantum theory may allow unbounded negative energy states, affecting black hole evaporation.

Abstract

We show that a whole class of quantum actions for dilaton-gravity, which reduce to the CGHS theory in the classical limit, can be written as a Liouville-like theory. In a sub-class of this, the field space singularity observed by several authors is absent, regardless of the number of matter fields, and in addition it is such that the dilaton-gravity functional integration range (the real line) transforms into itself for the Liouville theory fields. We also discuss some problems associated with the usual calculation of Hawking radiation, which stem from the neglect of back reaction. We give an alternative argument incorporating back reaction but find that the rate is still asymptotically constant. The latter is due to the fact that the quantum theory does not seem to have a lower bound in energy and Hawking radiation takes positive Bondi (or ADM) mass solutions to arbitrarily large negative mass.