Evaluating the Wald Entropy from two-derivative terms in quadratic actions

Abstract

We evaluate the Wald Noether charge entropy for a black hole in generalized theories of gravity. Expanding the Lagrangian to second order in gravitational perturbations, we show that contributions to the entropy density originate only from the coefficients of two-derivative terms. The same considerations are extended to include matter fields and to show that arbitrary powers of matter fields and their symmetrized covariant derivatives cannot contribute to the entropy density. We also explain how to use the linearized gravitational field equation rather than quadratic actions to obtain the same results. Several explicit examples are presented that allow us to clarify subtle points in the derivation and application of our method.

References in corpus (4)

• A Note on Thermodynamics of Black Holes in Lovelock Gravity
• The ratio of shear viscosity to entropy density in generalized theories of gravity
• Entropy density of spacetime and thermodynamic interpretation of field equations of gravity in any diffeomorphism invariant theory
• Higher dimensional black holes with a generalized gravitational action

Cited by in corpus (7)

• Warped AdS_3 Black Holes in Higher Derivative Gravity Theories
• Causality Violations in Lovelock Theories
• A Wald-like Formula for Energy
• Graviton n-point functions for UV-complete theories in Anti-de Sitter space
• Non-perturbative unitarity constraints on the ratio of shear viscosity to entropy density in UV complete theories with a gravity dual
• Lovelock gravity is equivalent to Einstein gravity coupled to form fields
• Gravitational entropy and thermodynamics away from the horizon