The entropy function for the extremal Kerr-(anti-)de Sitter black holes

Journal Article · Sun Aug 15 00:00:00 EDT 2010 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2010.02.002· OSTI ID:21455254

Cho, Jin-Ho ^[1]; Ko, Yumi ^[1]; Nam, Soonkeon ^[1]

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1. Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701 (Korea, Republic of)

Based on Sen's entropy function formalism, we consider the Bekenstein-Hawking entropy of the extremal Kerr-(anti-)de Sitter black holes in 4-dimensions. Unlike the extremal Kerr black hole case with flat asymptotic geometry, where the Bekenstein-Hawking entropy S is proportional to the angular momentum J, we get a quartic algebraic relation between S and J by using the known solution to the Einstein equation. We recover the same relation in the entropy function formalism. Instead of full geometry, we write down an ansatz for the near horizon geometry only. The exact form of the unknown functions and parameters in the ansatz are obtained by solving the differential equations which extremize the entropy function. The results agree with the nontrivial relation between S and J. We also study the Gauss-Bonnet correction to the entropy exploiting the entropy function formalism. We show that the term, though being topological thus does not affect the solution, contributes a constant addition to the entropy because the term shifts the Hamiltonian by that amount.

• OSTI ID: 21455254
• Journal Information: Annals of Physics (New York), Vol. 325, Issue 8; Other Information: DOI: 10.1016/j.aop.2010.02.002; PII: S0003-4916(10)00034-5; Copyright (c) 2010 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; ISSN 0003-4916
• Country of Publication: United States
• Language: English

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
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ASYMPTOTIC SOLUTIONS
BLACK HOLES
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SPACE
SYMMETRY GROUPS
THERMODYNAMIC PROPERTIES