New topological Gauss-Bonnet black holes in five dimensions

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 x 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 a and the cosmological constant A is fixed. For the second solution, the total energy is a constant and the entropy vanishes. These results expand our knowledge of both topological black holes in higher dimensions and the property of higher curvature corrections of gravitational theories.