On Geometric Entropy

TL;DR

This paper introduces a geometric entropy concept that explains the first quantum correction to black hole entropy, comparing Hamiltonian and Euclidean methods, and discusses divergences and string theory implications.

Contribution

It presents a geometric notion of entropy applicable in flat space that governs quantum corrections to black hole entropy, using two calculation methods and exploring divergences.

Findings

Quantum correction to black hole entropy is governed by geometric entropy.

Two calculation methods: Hamiltonian and Euclidean heat kernel.

Entropy diverges without an ultraviolet cutoff.

Abstract

We show that a geometrical notion of entropy, definable in flat space, governs the first quantum correction to the Bekenstein-Hawking black hole entropy. We describe two methods for calculating this entropy -- a straightforward Hamiltonian approach, and a less direct but more powerful Euclidean (heat kernel) method. The entropy diverges in quantum field theory in the absence of an ultraviolet cutoff. Various related finite quantities can be extracted with further work. We briefly discuss the corresponding question in string theory.