QUANTUM CORRECTIONS TO BLACK-HOLE ENTROPY IN STRING THEORY

The one-loop contribution to the entropy of a black hole from field mo des near the horizon is computed in string theory. It is modular invar iant and ultraviolet finite. There is an infrared divergence that sign ifies an instability near the event horizon of the black hole. It is d ue to the exponential growth of the density of states and the associat ed Hagedorn transition characteristic of string theory. It is argued t hat this divergence is indicative of a tree level contribution, and th e Bekenstein-Hawking-Gibbons formula for the entropy should be underst ood in terms of string states stuck near the horizon.