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.

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

References in corpus (4)

• Effective Field Theory for Inflation
• Local Fluid Dynamical Entropy from Gravity
• The zeroth law of black hole thermodynamics in arbitrary higher derivative theories of gravity
• Reparametrization Symmetry of Local Entropy Production on a Dynamical Horizon

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