Quantum Black Holes in Two Dimensions

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.