Abstract
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 Hořava-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 Hořava-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.
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