Quantum Evaporation of Liouville Black Holes

The classical field equations of a Liouville field coupled to gravity in two spacetime dimensions are shown to have black hole solutions. Exact solutions are also obtained when quantum corrections due to back reaction effects are included, modifying both the ADM mass and the black hole entropy. The thermodynamic limit breaks down before evaporation of the black hole is complete, indicating that higher-loop effects must be included for a full description of the process. A scenario for the final state of the black hole spacetime is suggested. Quantum Evaporation of Liouville Black Holes R.B. Mann Department of Physics University of Waterloo Waterloo, Ontario N2L 3G1 June 22, 1993 WATPHYS-TH93/01 hep-th/9307072 Liouville field theory has been a useful tool in expanding our understanding of 2D quantum gravity. The usual approach is to consider the Liouville field to be the conformal factor of the metric, whose quantum properties are then derived from the quantum dynamics of the Liouville field coupled to other 2D matter [1, 2]. Recently, however, a different approach has been adopted in which the Liouville field is taken be an independent matter field whose stress-energy couples to 2D gravity in a manner somewhat analogous to the (3+1)-dimensional case [3]. The field equations contain asymptotically flat black hole solutions whose temperature depends upon their ADM-mass, making them interesting objects of investigation. This letter presents the results of a study of the quantum dynamics of a Liouville field in curved two-dimensional spacetime; details will appear in a forthcoming paper [4]. Specifically, the classical field equations of a Liouville field in curved spacetime are modified to include quantum corrections due to both conformally coupled matter and to the gravity/Liouville system itself. An exact solution is obtained in each case, thereby fully incorporating the back-reaction into the classical black hole solution to one-loop order. The action is a particular version of dilaton gravity [5, 6] in which