ar X iv : h ep - t h / 05 04 14 1 v 1 18 A pr 2 00 5 Spacetime structure of static solutions in Gauss - Bonnet gravity : charged case
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چکیده
We have studied spacetime structures of static solutions in the n-dimensional Einstein-GaussBonnet-Maxwell-Λ system. Especially we focus on effects of the Maxwell charge. We assume that the Gauss-Bonnet coefficient α is non-negative and 4α̃/l ≤ 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 = rb > 0 for any mass parameter. There the Kretschmann invariant behaves as O((r− rb)), which is much milder than divergent behavior of the central singularity in general relativity O(r). In the k = 1 and 0 cases plus-branch solutions have no horizon. In the k = −1 case, the radius of a horizon is restricted as rh < √ 2α̃ (rh > √ 2α̃) in the plus (minus) branch. Some charged black hole solutions have no inner horizon in Gauss-Bonnet gravity. There are topological black hole solutions with zero and negative mass in the plus branch regardless of the sign of the cosmological constant. 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 ≥ 6 have an “inner” black hole, and inner and the “outer” black hole horizons. In the 4α̃/l = 1 case, only a positive mass solution is allowed, otherwise the metric function takes a complex value. Considering the evolution of black holes, we briefly discuss a classical discontinuous transition from one black hole spacetime to another.
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تاریخ انتشار 2005