Quasinormal modes of a static black hole in nonlinear electrodynamics

TL;DR

This paper studies how nonlinear electrodynamics affects the quasinormal modes of static AdS black holes, revealing that nonlinearity and charge influence oscillation and damping, breaking isospectrality and leading to purely imaginary modes under certain conditions.

Contribution

It introduces a numerical method to compute electromagnetic quasinormal modes of nonlinear electrodynamics black holes, highlighting the effects of nonlinearity on mode spectra and damping.

Findings

Increasing nonlinearity parameter $eta$ raises oscillation frequency and damping rate.

Nonlinear electrodynamics breaks isospectrality between electric and magnetic modes.

Large $eta$ and small magnetic charge lead to purely imaginary fundamental modes.

Abstract

We investigate the axial electromagnetic quasinormal modes of a static, asymptotically Anti--de Sitter (AdS) black hole sourced by a nonlinear electrodynamics model of Pleba\'{n}ski type. Starting from the master equation governing axial perturbations, we impose ingoing boundary conditions at the event horizon and normalizable (Dirichlet) behavior at the AdS boundary. Following the approach of Jansen, we recast the radial equation into a linear generalized eigenvalue problem by using an ingoing Eddington--Finkelstein formulation, compactifying the radial domain, and regularizing the asymptotic coefficients. The resulting problem is solved using a Chebyshev--Lobatto pseudospectral discretization. We compute the fundamental quasinormal mode frequencies for both the purely electric ($Q_m=0$) and purely magnetic ($Q_e=0$) sectors, emphasizing the role of the nonlinearity parameter $\beta$ and the effective charge magnitude $Q$. Our results show that increasing either $\beta$ or $Q$ raises both the oscillation frequency $\omega_R$ and the damping rate $-\omega_I$, leading to faster but more rapidly decaying ringdown profiles. Nonlinear electrodynamics breaks the isospectrality between electric and magnetic configurations: magnetic modes are systematically less oscillatory and more weakly damped than their electric counterparts. For sufficiently large $\beta$ and small $Q_m$, the fundamental mode becomes purely imaginary ($\omega_R \approx 0$), in agreement with the absence of a trapping potential barrier in this regime. These findings reveal qualitative signatures of nonlinear electromagnetic effects on black hole perturbations and may have implications for high-field or high-charge astrophysical environments.