Perturbations and quasinormal modes of black holes in general relativity coupled to nonlinear electrodynamics

Abstract

We investigate the quasinormal spectra and time-domain evolution of scalar, electromagnetic, and gravitational perturbations of the Einstein-Bronnikov black hole in Einstein gravity coupled to nonlinear electrodynamics. The effective potentials associated with all perturbation sectors are shown to form positive potential barriers that vanish at the event horizon and spatial infinity. Their height increases with the magnetic charge, while the scalar perturbation possesses the largest potential barrier. Unlike the Reissner-Nordström black hole, axial and polar electromagnetic perturbations are characterized by distinct effective potentials, demonstrating the breaking of isospectrality due to nonlinear electrodynamics. Quasinormal frequencies are computed using the sixth-order WKB approximation and the asymptotic iteration method, yielding excellent agreement for both fundamental and higher overtone modes. The oscillation frequencies increase monotonically with the magnetic charge, whereas the damping rates exhibit only moderate variations, confirming the linear stability of the Einstein-Bronnikov black hole under all perturbations considered. Time-domain profiles display exponentially damped ringdown signals consistent with the frequency-domain analysis. These results demonstrate that nonlinear electrodynamics leaves measurable imprints on black hole perturbations and may provide observational signatures for testing regular black hole geometries through future gravitational wave observations.