Topological black holes in Hořava-Lifshitz gravity

We find topological (charged) black holes whose horizon has an arbitrary constant scalar curvature 2k in Hořava-Lifshitz theory. Without loss of generality, one may take k=1, 0, and -1. The black hole solution is asymptotically anti–de Sitter with a nonstandard asymptotic behavior. Using the Hamiltonian approach, we define a finite mass associated with the solution. We discuss the thermodynamics of the topological black holes and find that the black hole entropy has a logarithmic term in addition to an area term. We find a duality in Hawking temperature between topological black holes in Hořava-Lifshitz theory and Einstein’s general relativity: the temperature behaviors of black holes with k=1, 0, and -1 in Hořava-Lifshitz theory are, respectively, dual to those of topological black holes with k=-1, 0, and 1 in Einstein’s general relativity. The topological black holes in Hořava-Lifshitz theory are thermodynamically stable.