BLACK-HOLE THERMODYNAMICS FROM QUANTUM-GRAVITY

The semiclassical approximation is studied on hypersurfaces approachin g the union of future null infinity and the event horizon on a large c lass of four-dimensional black hole backgrounds. Quantum fluctuations in the background geometry are shown to lead to a breakdown of the sem iclassical approximation in these models. The boundary of the region w here the semiclassical approximation breaks down is used to define a ' stretched horizon'. It is shown that the same effect that brings about the breakdown in semiclassical evolution associates a temperature and an entropy to the region behind the stretched horizon, and identifies the microstates that underlie the thermodynamical properties. The tem perature defined in this way is equal to that of the black hole and th e entropy is equal to the Bekenstein entropy up to a factor of order o ne.