Liouville models of black hole evaporation

A renormalizable two-dimensional quantum field theory, containing a metric, a dilaton and N massless scalar matter fields, has been proposed as a model for black hole evaporation reflecting the conformal anomaly. Previous work on this model has been done in the large-N (weak coupling) approximation and clear evidence for Hawking radiation and its back-reaction on the metric has been seen. There are, however, quantum consistency questions since the original model was only designed to be a c = 26 conformal field theory in the weak coupling limit. In this paper we construct new theories, differing from the old only in the dilaton dependence of the cosmological constant and reducing to it in the weak coupling limit. They are exact c = 26 conformal field theories and presumably consistent frameworks for discussing this problem. We also study the new theories with a change in the Polyakov action proposed by Strominger with a view to eliminating unphysical ghost Hawking radiation. The classical equations of motion of the new theories are explicitly soluble, thus permitting an exact analysis of both static solutions and dynamic scenarios. While the static solutions are, by and large, physically reasonable, the dynamical solutions include puzzling examples where wrong-sign Hawking radiation is stimulated by allowing matter to fall into a static solution. We indicate how the latter problem may be resolved in the full quantum theory.