Extremalization approach to black hole thermodynamics: perturbations around higher-derivative gravities

TL;DR

This paper extends the extremalization approach to compute first-order thermodynamic corrections for black holes in general higher-derivative gravity theories, avoiding explicit solution perturbations.

Contribution

It demonstrates that the extremalization method applies beyond Einstein gravity, enabling calculation of corrections in complex theories like Einstein--Gauss--Bonnet without solving perturbed solutions.

Findings

First-order thermodynamic corrections derived without explicit black hole solutions.

Method applicable to asymptotically flat and AdS spacetimes.

Extended extremalization approach to general higher-derivative gravities.

Abstract

When higher-derivative terms are added to a gravitational action, black hole solutions and their thermodynamic properties are generally corrected. Recent progress has shown that, by treating higher-derivative operators as perturbations, the first-order corrections to black hole thermodynamics can be obtained without explicit knowledge of the corresponding perturbed black hole solutions. This result can be understood as a consequence of an extremalization principle underlying the Euclidean action formulation of black hole thermodynamics. In this work, we emphasize that this extremalization approach is not restricted to perturbations around Einstein gravity. Instead, it can be applied to perturbations of more general higher-derivative gravity theories whose black hole solutions are already known and can be taken as the zeroth-order background. As an explicit illustration, we consider Einstein--Gauss--Bonnet gravity as the zeroth-order theory and study the first-order thermodynamic corrections induced by further higher-order curvature operators. We show that these corrections can be derived without solving the perturbed black hole solutions, both in asymptotically flat and asymptotically AdS spacetimes.