Charged scalar field instability between the event and cosmological horizons

TL;DR

This paper confirms and analyzes the instability of charged scalar fields around Reissner-Nordström-de Sitter black holes, showing it is superradiant in origin and depends on the cosmological constant and charges.

Contribution

It provides a detailed frequency-domain and time-domain analysis of the instability, establishing superradiance as a necessary condition and exploring parameter dependencies.

Findings

Instability occurs at small eQ values.

Critical eQ depends on the cosmological constant Λ.

All unstable modes are superradiant, but not all superradiant modes are unstable.

Abstract

Recently, a new interesting instability of a charged scalar field in the Reissner-Nordstr\"om-de Sitter background has been found (arXiv:1405.4931v2) through the time-domain integration of the perturbation equation. We investigate further properties of this instability, confirm its existence by concordant frequency-domain and time-domain calculations and show that it occurs at however small value of the coupling eQ, where e and Q are charges of a scalar field and black hole respectively. We also investigate the parametric region of instability and show that the critical values of eQ at which the stabilization happens strongly depends on the value of cosmological constant $\Lambda$ and softly on Q. We show that all the unstable modes are superradiant, but not all the superradiant modes are unstable. We analytically prove that superradiance is necessary (but not sufficient) condition for the instability in this case and, thereby, demonstrate the superradiant origin of the instability.