FINITE BLACK-HOLE ENTROPY AND STRING THEORY

An accelerating observer sees a thermal bath of radiation at the Hawki ng temperature which is proportional to the acceleration. Also, in str ing theory there is a Hagedorn temperature beyond which one cannot go without an infinite amount of energy. Several authors have shown that in the context of Hawking radiation a limiting temperature for string theory leads to a Limiting acceleration, which for a black hole implie s a minimum distance from the horizon for an observer to remain statio nary. We argue that this effectively introduces a cutoff in Rindler sp ace or the Schwarschild geometry inside of which accelerations would e xceed this maximum value. Furthermore, this natural cutoff in turn all ows one to define a finite entropy for Rindler space or a black hole a s all divergences were occurring on the horizlon. In all cases if a pa rticular relationship exists between Newton's constant and the string tension then the entropy of the string modes agrees with the Bekenstei n-Hawking formula.