Black-hole thermodynamics and renormalization

TL;DR

This paper investigates how ultraviolet divergences near black hole horizons depend on temperature, revealing topological corrections to entropy and emphasizing the need for renormalization to obtain finite thermodynamic quantities.

Contribution

It demonstrates the temperature dependence of ultraviolet divergences in black hole thermodynamics and identifies topological curvature corrections to black hole entropy.

Findings

Black hole entropy acquires a topological correction from horizon curvature.

Renormalization of surface constants is necessary for finite thermodynamic quantities.

Discrepancies exist between different regularization techniques.

Abstract

Ultraviolet regime in quantum theory with horizons, contrary to ordinary theory, depends on the temperature of the system due to additional surface divergences in the effective action. We evaluate their general one-loop structure paying attention to effects of the curvature of the space-time near the horizon. In particular, apart from the area term, the entropy of a black hole is shown to acquire a topological correction in the form of the integral curvature of the horizon. To get the entropy, heat capacity and other thermodynamical quantities finite, such a kind of singularities should be removed by renormalization of a number of constants in a surface functional introduced in the effective action at arbitrary temperature. We also discuss a discrepancy in the different regularization techniques.