On one-loop renormalization of black-hole entropy

TL;DR

This paper demonstrates that one-loop divergences in quantum black hole entropy can be fully removed through standard renormalization of gravitational parameters, accounting for higher curvature terms.

Contribution

It proves that higher order curvature terms in the effective gravitational action eliminate one-loop divergences in black hole entropy.

Findings

One-loop divergences are canceled by renormalization.

Higher curvature terms modify the entropy beyond Bekenstein-Hawking.

The proof relies on the geometry of the horizon surface.

Abstract

One-loop divergences appearing in the entropy of a quantum black hole are proven to be completely eliminated by the standard renormalization of both the gravitational constant and other coefficients by the $R^2$-terms in the effective gravitational action. The essential point of the proof is that due to the higher order curvature terms the entropy differs from the Bekenstein-Hawking one in the Einstein gravity by the contributions depending on the internal and external geometry of the horizon surface.