QUANTUM BLACK-HOLES IN 2 DIMENSIONS

We show that a whole class of quantum actions for dilaton gravity, which reduce to the Callan-Giddings-Harvey-Strominger theory in the classical limit, can be written as a Liouville-like theory. In a subclass 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 has no lower bound in energy and Hawking radiation takes positive Bondi (or Arnowitt-beser-Misner) mass solutions to an arbitrarily large negative mass.