Electromagnetic perturbations of black holes in general relativity coupled to nonlinear electrodynamics

TL;DR

This paper investigates electromagnetic perturbations of black holes in general relativity coupled with nonlinear electrodynamics, revealing differences in quasinormal modes compared to classical Maxwell theory and analyzing new NED black hole solutions.

Contribution

It introduces the study of EM perturbations in NED black holes, highlighting the relation to effective metrics and comparing QN spectra with Reissner-Nordström black holes.

Findings

Effective potentials relate to photon effective metrics, not spacetime metric.

QN frequencies differ between NED and Maxwell cases.

New NED black hole solutions reduce to Reissner-Nordström in the weak field limit.

Abstract

The electromagnetic (EM) perturbations of the black hole solutions in general relativity coupled to nonlinear electrodynamics (NED) are studied for both electrically and magnetically charged black holes, assuming that the EM perturbations do not alter the spacetime geometry. It is shown that the effective potentials of the electrically and magnetically charged black holes related to test perturbative NED EM fields are related to the effective metric governing the photon motion, contrary to the effective potential of the linear electrodynamic (Maxwell) field that is related to the spacetime metric. Consequently, corresponding quasinormal (QN) frequencies differ as well. As a special case, we study new family of the NED black hole solutions which tend in the weak field limit to the Maxwell field, giving the Reissner-Nordstr\"{o}m (RN) black hole solution. We compare the NED Maxwellian black hole QN spectra with the RN black hole QN spectra.