Stability of Reissner-Nordström black hole in de Sitter background under charged scalar perturbation

Abstract

We find a new instability in the four-dimensional Reissner-Nordstr\"om--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 a larger angular index, as explicitly proved for $l=1$. Our results are obtained from a numerical investigation of the time-domain profiles of the perturbations.