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

Corrections to Extremal Black Holes from Iyer-Wald Formalism