On the first order corrections to the black hole thermodynamics in higher curvature theories of gravity

Abstract

In modified theories of gravity, higher curvature terms may be added to the Einstein-Hilbert action. Conventionally, the effects of the higher curvature terms on the black hole thermodynamics are rather difficult to obtain. In this paper, we show that, at least at the first order level, the corrections to the thermodynamics of the Schwarzschild black hole can be easily obtained, without solving the modified black hole metric. We examine some specific examples, which produces the known results in the literature, as well as those previously unknown. Furthermore, we find some nonperturbative exact results by generalizing the first-order analysis. In particular, a novel relation between the Euclidean integrals of the Einstein--Hilbert term and the higher curvature terms is found and proved.

7 pages, no figures, the latest version accepted by PRD

References in corpus (4)

• Quantum Gravitational Corrections to the Entropy of a Schwarzschild Black Hole
• On Euclidean and Noetherian Entropies in AdS Space
• Logarithmic correction to black hole entropy from the nonlocality of quantum gravity
• Gauss-Bonnet black holes with non-constant curvature horizons

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