Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-11-02
Phys.Rev.D81:024018,2010
Physics
High Energy Physics
High Energy Physics - Theory
V2, Revtex4, 27 pages, no figures, some details and references added, to be published in Phys.Rev.D
Scientific paper
10.1103/PhysRevD.81.024018
We present a class of new black hole solutions in $D$-dimensional Lovelock gravity theory. The solutions have a form of direct product $\mathcal{M}^m \times \mathcal{H}^{n}$, where $D=m+n$, $\mathcal{H}^n$ is a negative constant curvature space, and are characterized by two integration constants. When $m=3$ and 4, these solutions reduce to the exact black hole solutions recently found by Maeda and Dadhich in Gauss-Bonnet gravity theory. We study thermodynamics of these black hole solutions. Although these black holes have a nonvanishing Hawking temperature, surprisingly, the mass of these solutions always vanishes. While the entropy also vanishes when $m$ is odd, it is a constant determined by Euler characteristic of $(m-2)$-dimensional cross section of black hole horizon when $m$ is even. We argue that the constant in the entropy should be thrown away. Namely, when $m$ is even, the entropy of these black holes also should vanish. We discuss the implications of these results.
Cai Rong-Gen
Cao Li-Ming
Ohta Nobuyoshi
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