A Universal Relation Between Corrections to Entropy and Extremality

TL;DR

This paper proves a universal thermodynamic relation linking corrections to black hole entropy and extremality bounds, suggesting a broad applicability beyond gravity and supporting Weak Gravity Conjecture-like behavior.

Contribution

It establishes a universal, purely thermodynamic relation between entropy and extremality corrections applicable beyond gravitational systems.

Findings

Positive entropy corrections decrease extremal black hole mass

Relation holds universally for various black hole types

Supports Weak Gravity Conjecture-like behavior

Abstract

Perturbative corrections to General Relativity alter the expressions for both the entropy of black holes and their extremality bounds. We prove a universal relation between the leading corrections to these quantities. The derivation is purely thermodynamic and the result also applies beyond the realm of gravitational systems. In scenarios where the correction to the entropy is positive, our result proves that the perturbations decrease the mass of extremal black holes, when holding all other extensive variables fixed in the comparison. This implies that the extremality relations of a wide class of black holes display Weak Gravity Conjecture-like behavior.