Higher derivative contributions to black hole thermodynamics at NNLO

Abstract

In an effective theory of gravity, thermodynamic quantities of black holes receive corrections from the infinite series of higher derivative terms. At the next to leading order, these can be obtained by using only the leading order solution. In this paper, we push forward this property to the next to next to leading order. We propose a formula which yields the Euclidean action of asymptotically flat black holes at the next to next to leading order using only the solution up to and including the next to leading order. Other conserved quantities are derived from the Euclidean action via standard thermodynamic relation. We verify our formula in examples of $D$-dimensional pure gravity and Einstein-Maxwell theory extended by 4- and 6-derivative terms. Based on our formula, we also prove that for asymptotically flat black holes, the physical quantities are invariant under field redefinitions.

Latex, 40 pages with 17-page appendices, references added

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• Dyonic Black Strings and the Charge Lattice in Salam-Sezgin model
• Black hole thermodynamics at 4 derivatives, natural variables and BPS limits
• Constraining Cubic Curvature Corrections to General Relativity with Quasi-Periodic Oscillations
• Quantum gravitational corrections to Reissner-Nordström black hole thermodynamics and their implications for the weak gravity conjecture
• Universality on thermodynamic relation with corrections in higher-dimensional de Sitter black holes
• Extremalization approach to black hole thermodynamics: perturbations around higher-derivative gravities
• Universality on thermodynamic relation with corrections in Einstein-Bel-Robinson gravity Black hole