Gauss-Bonnet black holes in a special anisotropic scaling spacetime

Abstract

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 $(t,r,{\theta }_i)\to ({\lambda }^{z}t,{\lambda }^{-1}r,{\lambda }^{x_i}{\theta }_i)$. Due to the anisotropic scaling dimension of the spatial coordinates, this spacetime does not support the full Schrödinger 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.

17 pages, 11 figures

References in corpus (14)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Quantum Gravity at a Lifshitz Point
• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Lectures on Holographic Superfluidity and Superconductivity
• Exact solutions for the Einstein-Gauss-Bonnet theory in five dimensions: Black holes, wormholes and spacetime horns
• Gauss-Bonnet Holographic Superconductors
• Simple compactifications and Black p-branes in Gauss-Bonnet and Lovelock Theories
• Quasi-Topological Lifshitz Black Holes
• Anisotropic fluid dynamics in the early stage of relativistic heavy-ion collisions
• Nonlinearly charged Lifshitz black holes for any exponent $z>1$
• Holographic thermalization in Gauss-Bonnet gravity with de Sitter boundary
• Physics of the cosmic microwave background anisotropy

Cited by in corpus (1)

• Noether gauge symmetry approach applying for the non-minimally coupled gravity to the Maxwell field