Spacetime structure of static solutions in Gauss-Bonnet gravity: charged case

Takashi Torii; Hideki Maeda

doi:10.1103/PhysRevD.72.064007

paper

Spacetime structure of static solutions in Gauss-Bonnet gravity: charged case

arXiv:hep-th/0504141 · doi:10.1103/PhysRevD.72.064007

Abstract

We have studied spacetime structures of static solutions in the $n$ -dimensional Einstein-Gauss-Bonnet-Maxwell- $Λ$ system. Especially we focus on effects of the Maxwell charge. We assume that the Gauss-Bonnet coefficient $α$ is non-negative and $4 α ~ / ℓ^{2} \leq 1$ in order to define the relevant vacuum state. Solutions have the $(n - 2)$ -dimensional Euclidean sub-manifold whose curvature is $k = 1, 0$ , or -1. In Gauss-Bonnet gravity, solutions are classified into plus and minus branches. In the plus branch all solutions have the same asymptotic structure as those in general relativity with a negative cosmological constant. The charge affects a central region of the spacetime. A branch singularity appears at the finite radius $r = r_{b} > 0$ for any mass parameter. There the Kretschmann invariant behaves as $O ((r - r_{b})^{- 3})$ , which is much milder than divergent behavior of the central singularity in general relativity $O (r^{- 4 (n - 2)})$ . Some charged black hole solutions have no inner horizon in Gauss-Bonnet gravity. Although there is a maximum mass for black hole solutions in the plus branch for $k = - 1$ in the neutral case, no such maximum exists in the charged case. The solutions in the plus branch with $k = - 1$ and $n \geq 6$ have an "inner" black hole, and inner and the "outer" black hole horizons. Considering the evolution of black holes, we briefly discuss a classical discontinuous transition from one black hole spacetime to another.

20 pages, 10 figures

Spacetime structure of static solutions in Gauss-Bonnet gravity: charged case

Abstract

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