Charged Dirac perturbations on Reissner-Nordstr\"om-Anti-de Sitter spacetimes: quasinormal modes with Robin boundary conditions

TL;DR

This paper investigates charged Dirac quasinormal modes in Reissner-Nordström-Anti-de Sitter black holes with Robin boundary conditions, revealing how electric charge influences the spectrum without causing superradiant instabilities.

Contribution

It extends previous work on neutral Dirac QNMs by deriving equations for charged fields and analyzing their spectra with Robin boundary conditions, including the effects of electric charge.

Findings

Charge coupling does not induce superradiant instabilities.

Electric charge significantly alters the Dirac QNM spectrum.

Vanishing energy flux boundary conditions apply to charged fields as well.

Abstract

We study charged Dirac quasinormal modes (QNMs) on Reissner-Nordstr\"om-Anti-de Sitter (RN-AdS) black holes with generic Robin boundary conditions, by extending our earlier work of neutral Dirac QNMs on Schwarzschild-AdS black holes. We first derive the equations of motion for charged Dirac fields on a RN-AdS background. To solve these equations we impose a requirement on the Dirac field: that its energy flux should vanish at asymptotic infinity. A set of two Robin boundary conditions compatible with QNMs is consequently found. By employing both analytic and numeric methods, we then obtain the quasinormal spectrum for charged Dirac fields, and analyse the impact of various parameters, in particular of electric charge. An analytic calculation shows explicitly that the charge coupling between the black hole and the Dirac field does not trigger superradiant instabilities. Numeric calculations, on the other hand, show quantiatively that Dirac QNMs may change substantially due to the electric charge. Our results illustrate how vanishing energy flux boundary conditions, as a generic principle, are applicable not only to neutral but also to electrically charged fields.