The instability spectra of near-extremal Reissner-Nordstr\"om-de Sitter black holes

TL;DR

This paper analytically investigates the unstable resonant modes of charged massive scalar fields in near-extremal Reissner-Nordström-de Sitter black holes, revealing exponential growth and providing a compact formula for the spectrum.

Contribution

It offers the first analytical derivation of the unstable quasinormal mode spectrum for charged scalar fields in near-extremal RNdS black holes using WKB analysis.

Findings

Unstable exponentially growing modes are characterized.

A compact analytical formula for the quasinormal spectrum is derived.

The system exhibits instability in the non-asymptotically flat case.

Abstract

The linearized dynamics of charged massive scalar fields in the near-extremal charged Reissner-Nordstr\"om-de Sitter (RNdS) black-hole spacetime is studied analytically. Interestingly, it is proved that the non-asymptotically flat charged black-hole-field system is characterized by {\it unstable} (exponentially growing in time) complex resonant modes. Using a WKB analysis in the eikonal large-mass regime $M\mu\gg1$, we provide a remarkably compact analytical formula for the quasinormal resonant spectrum $\{\omega_n(M,Q,\Lambda,\mu,q)\}_{n=0}^{n=\infty}$ which characterizes the unstable modes of the composed RNdS-black-hole-charged-massive-scalar-field system [here $\{M,Q,\Lambda\}$ are respectively the mass, electric charge, and cosmological constant of the black-hole spacetime, and $\{\mu,q\}$ are the proper mass and charge coupling constant of the linearized field].