The second law of black hole mechanics in effective field theory

Hollands, Stefan; Kovács, Áron D.; Reall, Harvey S.

doi:10.48550/arxiv.2205.15341

Cited by 1 publication

(1 citation statement)

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“…Further, Wall's formula does not agree with the Jacobson-Kang-Myers entropy [78] (which was shown to obey the second law) for arbitrary f (R) gravity; they only agree for R 2 theories in the linear approximation. For effective higher-curvature theories, Walls method was extended to higher order in perturbations by adding terms (at least) quadratic in quantities with positive boost weight [79][80][81].…”

Section: Quantum Correctionsmentioning

confidence: 99%

Cornering gravitational entropy

Kastikainen,

Svesko

2024

J. High Energ. Phys.

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We present a new derivation of gravitational entropy functionals in higher-curvature theories of gravity using corner terms that are needed to ensure well-posedness of the variational principle in the presence of corners. This is accomplished by cutting open a manifold with a conical singularity into a wedge with boundaries intersecting at a corner. Notably, our observation provides a rigorous definition of the action of a conical singularity that does not require regularization. For Einstein gravity, we compute the Rényi entropy of gravitational states with either fixed-periodicity or fixed-area boundary conditions. The entropy functional for fixed-area states is equal to the corner term, whose extremization follows from the variation of the Einstein action of the wedge under transverse diffeomorphisms. For general Lovelock gravity the entropy functional of fixed-periodicity states is equal to the Jacobson-Myers (JM) functional, while fixed-area states generalize to fixed-JM-functional states, having a flat spectrum. Extremization of the JM functional is shown to coincide with the variation of the Lovelock action of the wedge. For arbitrary F(Riemann) gravity, under special periodic boundary conditions, we recover the Dong-Lewkowycz entropy for fixed-periodicity states. Since the variational problem in the presence of corners is not well-posed, we conjecture the generalization of fixed-area states does not exist for such theories without additional boundary conditions. Thus, our work suggests the existence of entropy functionals is tied to the existence of corner terms which make the Dirichlet variational problem well-posed.

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Section: Quantum Correctionsmentioning

confidence: 99%