Seiberg-Witten Instability of Various Topological Black Holes

TL;DR

This paper reviews the Seiberg-Witten instability in topological black holes within Anti-de Sitter space, highlighting how certain black holes exhibit instabilities at finite distances from the horizon due to brane pair nucleation.

Contribution

It compares the instability phenomena across different theories, including general relativity, Hořava-Lifshitz gravity, and string theory, revealing unique and shared instability behaviors.

Findings

Topological black holes in AdS space exhibit Seiberg-Witten instability.

Instabilities in Hořava-Lifshitz black holes occur at finite distances from the horizon.

Similar instability patterns are observed in string theory black hole models.

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 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.