Black hole entropy without brick walls

We present evidence which confirms a suggestion by Susskind and Uglum regarding black hole entropy. Using a Pauli-Villars regulator, we find that 't Hooft's approach to evaluating black hole entropy through a statistical-mechanical counting of states for a scalar field propagating outside the event horizon yields precisely the one-loop renormalization of the standard Bekenstein-Hawking formula S=scrA/(4G). Our calculation also yields a constant contribution to the black hole entropy, a contribution associated with the one-loop renormalization of higher curvature terms in the gravitational action.