  We review the Seiberg-Witten instability of topological black holes in
Anti-de Sitter space due to nucleation of brane-anti-brane pairs. We start with
black holes in general relativity, and then proceed to discuss the peculiar
property of topological black holes in Ho\v{r}ava-Lifshitz gravity -- they have
instabilities that occur at only finite range of distance away from the
horizon. This behavior is not unique to black holes in Ho\v{r}ava-Lifshitz
theory, as it is also found in the relatively simple systems of charged black
hole with dilaton hair that arise in low energy limit of string theory.
