Instability of de Sitter Reissner-Nordstrom black hole in the 1/D expansion

TL;DR

This paper investigates the stability of large D charged de Sitter black holes, revealing an instability at high charge and the emergence of non-spherical solutions, advancing understanding of black hole phase structures in higher dimensions.

Contribution

It demonstrates the instability of de Sitter Reissner-Nordstrom black holes at high charge and constructs non-spherical static solutions using large D effective theory.

Findings

Black holes become unstable at high charge in higher dimensions.

Existence of non-spherical static solutions at critical charge.

Identification of zero-mode static perturbations indicating phase transitions.

Abstract

We study large D effective theory for D dimensional charged (Anti) de Sitter black holes. Then we show that de Sitter Reissner-Nordstrom black hole becomes unstable against gravitational perturbations at larger charge than certain critical value in higher dimension. Furthermore we find that there is a non-trivial zero-mode static perturbation at the critical charge. The existence of static perturbations suggests the appearance of non-spherical symmetric solution branches of static charged de Sitter black hole. This expectation is confirmed by constructing the non-spherical symmetric static solutions of large D effective equations.