Lovelock black holes with maximally symmetric horizons
Mar, 201150 pages
Published in:
- Class.Quant.Grav. 28 (2011) 165005
e-Print:
- 1103.4184 [gr-qc]
Report number:
- CECS-PHY-11-02
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Abstract: (arXiv)
We investigate some properties of n(\ge 4)-dimensional spacetimes having symmetries corresponding to the isometries of an (n-2)-dimensional maximally symmetric space in Lovelock gravity under the null or dominant energy condition. The well-posedness of the generalized Misner-Sharp quasi-local mass proposed in the past study is shown. Using this quasi-local mass, we clarify the basic properties of the dynamical black holes defined by a future outer trapping horizon under certain assumptions on the Lovelock coupling constants. The C^2 vacuum solutions are classified into four types: (i) Schwarzschild-Tangherlini-type solution/ (ii) Nariai-type solution/ (iii) special degenerate vacuum solution/ (iv) exceptional vacuum solution. The conditions for the realization of the last two solutions are clarified. The Schwarzschild-Tangherlini-type solution is studied in detail. We prove the first law of black-hole thermodynamics and present the expressions for the heat capacity and the free energy.Note:
- 50 pages, no figure/ v2, revised version. Section 4.2 on exact solutions with matter added. Propositions 17 and 19 and Appendix B improved. References added/ v3, Proposition 20 added. Accepted for publication in Classical and Quantum Gravity
- black hole: thermodynamics
- gravitation: Lovelock
- space-time: Tangherlini
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