Liouville models of black hole evaporation

27 pages, revised ("Note Added" is expanded to show how careful treatment of quantum effects makes the Hawking radiation rate proportional to N/12 rather than (N-24)/12 and also to show that the cosmic censorship mechanism proposed by Russo et.al. for a somewhat different model works for our model as well. New references are added and the preprint number is corrected.) PUPT-1320International audienceWe construct new theories of dilation gravity coupled to conformal matter which are exact $c=26$ conformal field theories and presumably consistent frameworks for discussing black hole physics in two dimensions. They differ from the CGHS equations in the precise dilaton dependence of the cosmological constant. A further modification proposed by Strominger with a view to eliminating unphysical ghost Hawking radiation is also considered. The new classical equations of motion are explicitly soluble, thus permitting an exact analysis of both static and dynamic senarios. While the static solutions are physically reasonable, the dynamical solutions include puzzling examples with wrong-sign Hawking radiation. We indicate how the latter problem may be resolved in the full quantum theory