Corrections to Extremal Black Holes from Iyer-Wald Formalism

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.

8 pages, 1 figure. v2: Minor clarifications, added reference. Matches published version

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• Convexity of Charged Operators in CFTs with Multiple Abelian Symmetries
• The extremal Kerr entropy in higher-derivative gravities
• Black Hole Extremality in Nonlinear Electrodynamics: A Lesson for Weak Gravity and Festina Lente Bounds
• Gravitational Waves on Charged Black Hole Backgrounds in Modified Gravity
• Planar Black Holes as a Route to Understanding the Weak Gravity Conjecture
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• ISCOs and the weak gravity conjecture bound in higher derivative theories of gravity