Massive scalar perturbations and spectral signatures of the Bardeen regular black hole

We investigate massive scalar-field perturbations in the spacetime of the static Bardeen regular black hole. The Bardeen geometry, interpreted as a nonsingular black-hole solution supported by nonlinear electrodynamics, provides a useful setting for studying how regular cores modify the characteristic ringing and late-time response of compact objects. For a representative two-horizon configuration with M = 1 and magnetic charge g = 0 . 70 , we derive the Regge–Wheeler-type master equation from the minimally coupled Klein–Gordon equation and analyze the corresponding effective potential. The potential vanishes at the event horizon and approaches μ 2 at spatial infinity, reflecting the essential role of the scalar-field mass in the boundary-value problem. Quasinormal frequencies are computed using a Leaver–Frobenius pseudospectral method, while complementary time-domain evolutions are used to identify the prompt response, damped ringing stage, and late-time massive tails. The numerical results show that increasing the scalar-field mass raises the real part of the fundamental frequency and decreases the damping rate, indicating a systematic approach toward a long-lived quasi-resonant regime. The time-domain profiles exhibit oscillatory inverse-power tails consistent with the expected intermediate massive-field behavior. We also provide diagnostic grey-body-factor estimates based on the QNM–grey-body correspondence, showing that larger field mass suppresses low-frequency transmission and shifts the effective transmission threshold upward. The results constitute a fixed-configuration numerical dataset for massive scalar perturbations of the Bardeen regular black hole with M = 1 and g = 0 . 70 , obtained within the Leaver–Frobenius pseudospectral formulation and supported by internal truncation, residual, and time-domain consistency checks.

Hali tarjima qilinmagan