New Topological Gauss-Bonnet Black Holes in Five Dimensions

TL;DR

This paper explores novel five-dimensional topological black hole solutions in Einstein-Gauss-Bonnet gravity, analyzing their thermodynamic properties and revealing new insights into higher-dimensional and higher-curvature gravitational theories.

Contribution

It introduces new topological black hole solutions with nontrivial horizons and examines their thermodynamic stability and properties, expanding understanding of higher-dimensional gravity with curvature corrections.

Findings

First solution has negative specific heat, indicating thermodynamic instability.

Second solution's energy and entropy vanish, with fixed product of coupling constants.

Enlarges knowledge of topological black holes and higher curvature effects.

Abstract

We investigate vacuum static black hole solutions of Einstein-Gauss-Bonnet gravity with a negative cosmological constant in five dimensions. These are solutions with horizons of nontrivial topologies. The first one possesses a horizon with the topology $S^1 \times H^2$, and a varying Gauss-Bonnet coupling constant $\alpha$. By looking into its thermodynamic properties, we find that its specific heat capacity with fixed volume is negative, therefore it is thermodynamically unstable. The second one is equipped with a so-called "Sol-manifold" as its horizon, and interestingly, the product of the Gauss-Bonnet coupling constant $\alpha$ and the cosmological constant $\Lambda$ is fixed. For the second solution, the total energy and entropy vanish. These results enlarge our knowledge of both topological black holes in higher dimensions and the property of higher curvature corrections of gravitational theories.