Corrections to Extremal Black Holes from Iyer-Wald Formalism

TL;DR

This paper introduces a general method using the Iyer-Wald formalism to compute how perturbations affect the extremality and entropy of Kerr-Newman black holes, linking energy conditions to the weak gravity conjecture.

Contribution

It provides a novel integral-based approach to calculate extremality corrections and clarifies the role of energy conditions in black hole physics.

Findings

Corrections to extremality bounds are expressed via an effective stress tensor.

Violating the dominant energy condition can decrease black hole mass, supporting the weak gravity conjecture.

Applied method to higher-derivative corrections in AdS and Kerr black holes.

Abstract

We present a general method of computing corrections to the extremality bound and entropy of Kerr-Newman black holes due to an arbitrary perturbation using the Iyer-Wald formalism. In this method, corrections to the extremality bound are given by an integral over an effective stress tensor which, in particular cases of interest, reduces to the usual stress tensor. This clarifies the relation between extremality corrections and energy conditions. In particular, we show that a necessary condition to decrease the mass of an extremal black hole in a canonical ensemble, as required by the weak gravity conjecture, is that the perturbation violates the dominant energy condition. As an application of our method, we compute higher-derivative corrections to charged black holes in anti-de Sitter space and Kerr black holes.