Quasinormal modes of a static black hole in nonlinear electrodynamics

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 Plebański 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 ( $$Q_m=0$$ Q m = 0 ) and purely magnetic ( $$Q_e=0$$ Q e = 0 ) sectors, emphasizing the role of the nonlinearity parameter $$\beta $$ β and the effective charge magnitude Q . Our results show that increasing the nonlinear coupling $$\beta $$ β and, more generally, increasing the charge magnitude Q , tends to raise the oscillation frequency $$\omega _R$$ ω R and typically enhances the damping rate $$-\omega _I$$ - ω I , leading to faster but more rapidly decaying ringdown profiles. Nonlinear electrodynamics breaks the electric–magnetic spectral degeneracy: magnetic modes are systematically less oscillatory and more weakly damped than their electric counterparts. For sufficiently large $$\beta $$ β and small $$Q_m$$ Q m , the fundamental mode becomes purely imaginary ( $$\omega _R \approx 0$$ ω R ≈ 0 ), consistent with the disappearance of the trapping barrier in this regime. These findings reveal qualitative signatures of nonlinear electromagnetic effects on black hole perturbations and may provide useful theoretical insight into strong-field or high-charge astrophysical environments.