Renormalization of Black Hole Entropy

TL;DR

This paper reviews how the renormalization process affects black hole entropy calculations, showing that the total entropy aligns with the area law only in specific black hole dimensions, and discusses the microscopic origins of entropy.

Contribution

It provides a detailed analysis of the renormalization of black hole entropy and highlights dimensional dependencies in the area law validity.

Findings

Total entropy matches the area law for even-dimensional Reissner-Nordström black holes.

Renormalization affects the statistical and geometric entropy contributions.

Discussion on the microscopic origin of black hole entropy.

Abstract

We review the renormalization of one-loop effective action for gravity coupled to a scalar field and that of the Bekenstein-Hawking entropy of a black hole plus the statistical entropy of the scalar field. It is found that the total entropy of the black hole's geometric entropy and the statistical entropy yields the renormalized Bekenstein-Hawking area-law of black hole entropy only for even dimensional Reissner-N\"{o}rdstrom (Schwarzschild) black holes. We discuss the problem of the microscopic origin of black hole entropy in connection with the renormalization of black hole entropy.