Horizon instability of extremal Reissner-Nordstr\"om black holes to charged perturbations

TL;DR

This paper studies the stability of highly charged Reissner-Nordstr"om black holes against charged scalar perturbations, revealing a near-horizon transient instability that becomes the Aretakis instability in the extremal limit, linked to shared symmetries.

Contribution

It demonstrates the presence of a transient near-horizon instability in charged black holes and connects it to the Aretakis instability and near-horizon symmetries.

Findings

Transient instability in near-horizon region of charged black holes

Matching of instability rates with Kerr solutions

Shared near-horizon symmetry explains the results

Abstract

We investigate the stability of highly charged Reissner-Nordstr\"om black holes to charged scalar perturbations. We show that the near-horizon region exhibits a transient instability which becomes the Aretakis instability in the extremal limit. The rates we obtain match the enhanced rates for nonaxisymmetric perturbations of the near-extremal and extremal Kerr solutions. The agreement is shown to arise from a shared near-horizon symmetry of the two scenarios.