An action for the exact string black hole

TL;DR

This paper constructs a local action describing the exact 2D string black hole, analyzing its properties, dualities, and implications for black hole thermodynamics and string theory.

Contribution

It introduces a specific 2D Maxwell-dilaton gravity action for the exact string black hole, exploring its constants of motion, thermodynamics, dualities, and potential extensions.

Findings

Derived ADM mass, Hawking temperature, and entropy for the black hole.

Identified a dual action describing the naked singularity via branch ambiguity.

Connected the strong coupling limit to the 5D Schwarzschild 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.