Black Hole Entropy without Brick Walls

TL;DR

This paper confirms that black hole entropy can be derived from quantum field theory without the need for a brick wall cutoff, showing it matches the Bekenstein-Hawking formula and includes quantum corrections.

Contribution

It demonstrates that 't Hooft's statistical-mechanical approach reproduces the Bekenstein-Hawking entropy and accounts for quantum corrections without a brick wall.

Findings

Black hole entropy matches the Bekenstein-Hawking formula.

Quantum corrections arise from higher curvature terms.

No brick wall cutoff is necessary for entropy calculation.

Abstract

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, $S=\A/(4G)$. 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.