Dynamical behavior of the $C$-metric: charged scalar fields, quasinormal modes and superradiance

TL;DR

This paper investigates the complex quasinormal modes and superradiance phenomena of charged scalar fields around accelerating black holes described by the charged $C$-metric, revealing new dynamical behaviors due to scalar charge and acceleration effects.

Contribution

It extends quasinormal mode analysis to charged scalar fields in the charged $C$-metric and uncovers how scalar charge influences mode deformation and superradiant amplification.

Findings

Photon surface modes deform with scalar charge.

Acceleration and near-extremal modes gain oscillations when charged.

Superradiant amplification is enhanced despite reduced frequency range.

Abstract

The $C$-metric is a boost-symmetric spacetime solution to the vacuum Einstein field equations which describes black holes that are uniformly accelerated under the tension of a cosmic string. Only recently the thermodynamics of accelerating black holes and their modal stability against neutral scalar perturbations were concisely established. The generalization of accelerating black holes to incorporate an electric charge, namely the charged $C$-metric, possess three distinct families of quasinormal mode frequencies; the complex photon surface quasinormal modes associated with unstable null particles at the equatorial plane of the photon surface, the purely imaginary acceleration modes whose existence solely depends on the acceleration of spacetime and the purely imaginary near-extremal modes which dominate the dynamics of the ringdown at late times when the event and Cauchy horizon approach each other. We extend the quasinormal mode analysis to charged scalar fluctuations and find that the photon surface modes are continuously deformed with respect to their neutral counterpart as the scalar charge is increased. We further find that the acceleration and near-extremal families acquire an oscillation frequency when the scalar charge is introduced. Finally, we study the superradiant amplification of charged scalar monochromatic waves impinging charged accelerating black holes. We find that even though the frequency range of superradiant amplification is lessened due to the acceleration, the amplification factors are considerably elevated with respect to those transpiring in Reissner-Nordstr\"om black holes and are maximized when the scalar charge is significantly large.