String theory formulation of the three-dimensional black hole

Abstract

A black hole solution to three-dimensional general relativity with a negative cosmological constant has recently been found. We show that a slight modification of this solution yields an exact solution to string theory. This black hole is equivalent (under duality) to the previously discussed three-dimensional black string solution. Since the black string is asymptotically flat and the black hole is asymptotically anti--de Sitter, this suggests that strings are not affected by a negative cosmological constant in three dimensions.