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

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 4α˜/ℓ²≤1 in order to define the relevant vacuum state. Solutions have the (n-2)-dimensional Euclidean submanifold 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 a 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 the divergent behavior of the central singularity in general relativity O(r^-4(n-2)). 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 r_h<√2α˜ (r_h>√2α˜) 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 outer black hole horizons. In the 4α˜/ℓ²=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.