Topological black holes in Hořava-Lifshitz gravity
Abstract
We find topological (charged) black holes whose horizon has an arbitrary constant scalar curvature $2k$ in Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz theory. Without loss of generality, one may take $k=1$, 0, and $\ensuremath{-}1$. 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 Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz theory and Einstein's general relativity: the temperature behaviors of black holes with $k=1$, 0, and $\ensuremath{-}1$ in Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz theory are, respectively, dual to those of topological black holes with $k=\ensuremath{-}1$, 0, and 1 in Einstein's general relativity. The topological black holes in Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz theory are thermodynamically stable.