The second law of black hole mechanics in effective field theory

Abstract

We investigate the second law of black hole mechanics in gravitational theories with higher derivative terms in the action. Wall has described a method for defining an entropy that satisfies the second law to linear order in perturbations around a stationary black hole. We show that this can be extended to define an entropy that satisfies the second law to quadratic order in perturbations, provided that one treats the higher derivative terms in the sense of effective field theory. We also address some outstanding issues with Wall's method, in particular, its gauge invariance and its relation to the Iyer-Wald entropy.

arXiv comment57 pages + Appendix; v2: typos corrected, references added; v3: argument of section 4 simplified, typos corrected

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• Generalized Second Law for Non-minimally Coupled Matter Theories
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• Entanglement Entropy and Thermodynamics of Dynamical Black Holes
• New Horizons in Effective Field Theory?