The Entropy Sum of (A)dS Black Holes in Four and Higher Dimensions

Abstract

We present the "entropy sum" relation of (A)dS charged black holes in higher dimensional Einstein-Maxwell gravity, $f(R)$ gravity, Gauss-Bonnet gravity and gauged supergravity. For their "entropy sum" with the necessary effect of the un-physical "virtual" horizon included, we conclude the general results that the cosmological constant dependence and Gauss-Bonnet coupling constant dependence do hold in both the four and six dimensions, while the "entropy sum" is always vanishing in odd dimensions. Furthermore, the "entropy sum" of all horizons is related to the geometry of the horizons in four and six dimensions. In these explicitly four cases, one also finds that the conserved charges $M$ (the mass), $Q$ (the charge from Maxwell field or supergravity) and the parameter $a$ (the angular momentum) play no role in the "entropy sum" relations.

19 pages, 0 figures, some references added, conclusions improved, an appendix added, correct typos, published version

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Cited by in corpus (11)

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• Regular Multi-Horizon Black Holes in Modified Gravity with Non-Linear Electrodynamics
• The Entropy Relations of Black Holes with Multihorizons in Higher Dimensions
• The Universal Property of the Entropy Sum of Black Holes in All Dimensions
• Quantum-corrected two-dimensional Horava-Lifshitz black hole entropy
• Thermodynamic relations for entropy and temperature of multi-horizons black holes
• Emergent Black Hole Thermodynamics from Monodromy
• Generalized Hot Attractors
• Universal entropy relations: entropy formulae and entropy bound
• Notes on sums over horizons
• Angular Momentum-Free of the Entropy Relations for Rotating Kaluza-Klein Black Holes