Thermodynamical and perturbative signatures of the regular ABG black hole in a PFDM geometry

We focus on the gravitation quasi-normal modes of the Ayón-Beato García (ABG) black hole, which is a regular geometry formulation of Einstein’s equations with non-linear electrodynamics and without singularities. The corresponding geometry has a comparable general framework to the Reissner-Nordström black hole, with the exception that the Reissner-Nordström solution’s center singularity is replaced with a smooth, regular geometry, and r=0 corresponds to the origin in spherical coordinates [1]. We use the shadow data of the M87* black hole found by the Event Horizon Telescope to calculate the shadow radius associated with ABG black holes. We have found that the upper bound of the parameter ξ is −0.22 for lower charge X. We determine that the shadow radius decreases monotonically with the increase of the charge X. Moreover, we present some critical observations regarding the effect of X and ξ parameter on the potential barrier in the black hole geometry. In particular, we establish how these parameters influence the energy dissipating characteristics and the response frequency of the external perturbations. Finally, we compute the quasi-normal mode frequencies of scalar and electromagnetic field perturbations using the sixth order WKB method and provide qualitative visualization of the perturbation decay by time-domain simulations. Our results show that the scalar waves decay faster and then slower with the increase of the charge X and perfect fluid dark matter parameter ξ. Quasi-normal modes stay negative during the whole studied parameter range, which confirms the dynamic stability under scalar and electromagnetic perturbations. Moreover, this study reports a noticeable difference in the sensitivity of the perturbations caused by the scalar and electromagnetic field changes in the parameters.