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

TL;DR

This paper analyzes static solutions in higher-dimensional Einstein-Gauss-Bonnet-Maxwell gravity, focusing on how charge influences spacetime structures, singularities, and horizons, revealing new features like branch singularities and the absence of inner horizons in certain cases.

Contribution

It provides a detailed classification of charged static solutions in Gauss-Bonnet gravity, highlighting effects of charge on singularities and horizons, and introduces the concept of branch singularities and their properties.

Findings

Branch singularities occur at finite radius with milder divergence than in GR.

Charged solutions can lack inner horizons, unlike in Einstein gravity.

Solutions exhibit different asymptotic behaviors depending on the branch and parameters.

Abstract

We have studied spacetime structures of static solutions in the $n$-dimensional Einstein-Gauss-Bonnet-Maxwell-$\Lambda$ system. Especially we focus on effects of the Maxwell charge. We assume that the Gauss-Bonnet coefficient $\alpha$ is non-negative and $4{\tilde \alpha}/\ell^2\leq 1$ 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 $n\geq6$ 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.