Stability of Reissner-Nordstr\"om black hole in de Sitter background under charged scalar perturbation

TL;DR

This paper discovers a superradiant instability in four-dimensional Reissner-Nordstrom-de Sitter black holes caused by charged scalar perturbations with zero angular momentum, confirmed through numerical time domain analysis.

Contribution

It identifies a new superradiant instability specific to charged scalar perturbations with zero angular momentum in Reissner-Nordstrom-de Sitter black holes, expanding understanding of their stability.

Findings

Instability occurs for l=0 perturbations due to superradiance.

No instability found for l=1 perturbations.

Numerical time domain analysis confirms the instability.

Abstract

We find a new instability in the four-dimensional Reissner-Nordstrom-de Sitter black holes against charged scalar perturbations with vanishing angular momentum, $l=0$. We show that such an instability is caused by superradiance. The instability does not occur for an larger angular index, as explicitely proven for $l=1$. Our results are obtained from a numerical investigation of the time domain profiles of the perturbations.