On the first order corrections to the black hole thermodynamics in higher curvature theories of gravity

TL;DR

This paper presents a simplified method to compute first-order corrections to black hole thermodynamics in higher curvature gravity theories, revealing new relations and extending known results without solving complex metrics.

Contribution

It introduces a first-order approach to evaluate black hole thermodynamics corrections in higher curvature theories, including new exact relations and previously unknown results.

Findings

Derived first-order corrections without solving modified metrics

Established a novel relation between Euclidean integrals of different curvature terms

Extended known results and discovered new nonperturbative relations

Abstract

In modified theories of gravity, higher curvature terms may be added to the Einstein-Hilbert action. Conventionally, the effects of the higher curvature terms on the black hole thermodynamics are rather difficult to obtain. In this paper, we show that, at least at the first order level, the corrections to the thermodynamics of the Schwarzschild black hole can be easily obtained, without solving the modified black hole metric. We examine some specific examples, which produces the known results in the literature, as well as those previously unknown. Furthermore, we find some nonperturbative exact results by generalizing the first-order analysis. In particular, a novel relation between the Euclidean integrals of the Einstein--Hilbert term and the higher curvature terms is found and proved.