BLACK-HOLE ENTROPY IN CANONICAL QUANTUM-GRAVITY AND SUPERSTRING THEORY

In this paper the entropy of an eternal Schwarzschild black hole is st udied in the limit of an infinite black hole mass. The problem is addr essed from the point of view of both canonical quantum gravity and sup erstring theory. The entropy per unit area of a free scalar field prop agating in a fixed black hole background is shown to be quadratically divergent near the horizon. It is shown that such quantum corrections to the entropy per unit area are equivalent to the quantum corrections to the gravitational coupling. Unlike field theory, superstring theor y provides a set of identifiable configurations which give rise to the classical contribution to the entropy per unit area. These configurat ions can be understood as open superstrings with both ends attached to the horizon. The entropy per unit area is shown to be finite to all o rders in superstring perturbation theory. The importance of these conc lusions to the resolution of the problem of black hole information los s is reiterated.