Gauss-Bonnet black holes in a special anisotropic scaling spacetime

Inspired by the Lifshitz gravity as a theory with anisotropic scaling behavior, we suggest a new (n + 1)-dimensional metric in which the time and spatial coordinates scale anisotropically as (t, r, theta(i)) -> (lambda(z)t, lambda(-1)r, lambda(xi)theta(i)). Due to the anisotropic scaling dimension of the spatial coordinates, this spacetime does not support the full Schrodinger symmetry group. We look for the analytical solution of Gauss-Bonnet gravity in the context of the mentioned geometry. We show that Gauss-Bonnet gravity admits an analytical solution provided that the constants of the theory are properly adjusted. We obtain an exact vacuum solution, independent of the value of the dynamical exponent z, which is a black hole solution for the pseudo-hyperbolic horizon structure and a naked singularity for the pseudo-spherical boundary. We also obtain another exact solution of Gauss-Bonnet gravity under certain conditions. After investigating some geometrical properties of the obtained solutions, we consider the thermodynamic properties of these topological black holes and study the stability of the obtained solutions for each geometrical structure.

Automated summary

Inspired by Lifshitz gravity, this study proposes a new metric model that describes the anisotropic scaling behavior of spacetime. By investigating the analytical solutions of Gauss-Bonnet gravity in this geometric background, it is found that exact vacuum solutions and other solutions can be obtained by adjusting the constants properly. The geometrical properties, thermodynamic properties, and stability of the obtained solutions are also examined.