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.