The Fate of Instability of de Sitter Black Holes at Large $D$

TL;DR

This paper investigates the nonlinear gravitational instabilities of certain higher-dimensional black holes using large D expansion, revealing threshold behaviors and potential transitions to localized black hole solutions.

Contribution

It provides a nonlinear analysis of black hole instabilities at large D, identifying stationary lumpy solutions and possible transitions to localized black holes.

Findings

Thresholds of instability match linear analysis.

Unstable solutions evolve into stationary lumpy black holes.

Highly time-dependent solutions resemble black spots and rings.

Abstract

We study non-linearly the gravitational instabilities of Reissner-Nordstrom-de Sitter and Gauss-Bonnet-de Sitter black holes by using the large $D$ expansion method. In both cases, the thresholds of the instability are found to be consistent with the linear analysis, and on the thresholds the evolutions of the black holes under perturbations settle down to stationary lumpy solutions. However, the solutions in unstable region are highly time-dependent, and resemble the fully localized black spots and black ring with $S^{D-2}$ and $S^1\times S^{D-3}$ topologies, respectively. Our study indicates the possible transition between the lumpy black holes and localized black holes in higher dimensions.