An action for the exact string black hole

Abstract

A local action is constructed describing the exact string black hole discovered by Dijkgraaf, Verlinde and Verlinde in 1992. It turns out to be a special 2D Maxwell-dilaton gravity theory, linear in curvature and field strength. Two constants of motion exist: mass M>1, determined by the level k, and U(1)-charge Q>0, determined by the value of the dilaton at the origin. ADM mass, Hawking temperature T_H \propto \sqrt{1-1/M} and Bekenstein-Hawking entropy are derived and studied in detail. Winding/momentum mode duality implies the existence of a similar action, arising from a branch ambiguity, which describes the exact string naked singularity. In the strong coupling limit the solution dual to AdS_2 is found to be the 5D Schwarzschild black hole. Some applications to black hole thermodynamics and 2D string theory are discussed and generalizations - supersymmetric extension, coupling to matter and critical collapse, quantization - are pointed out.