Gravito-electromagnetic perturbations and QNMs of regular black holes

Abstract

In the framework of Einstein's gravity coupled to nonlinear electromagnetic fields, we study gravito-electromagnetic perturbations of magnetic regular black holes. The master equations of perturbations are obtained through Chandrasekhar's formulation, from which it can be seen, different from the electric counterparts, for magnetic black holes gravitational perturbations with odd-parity coupled only to the electromagnetic perturbations with even-parity. We solve the master equations numerically and obtain quasinormal modes (QNMs) for three typical regular black holes. Results show that QNMs of distinct regular black holes differ significantly, and they differ from that of the Reissner-Nordstr¨om black hole as well. Indications of these results on the stability of these regular black holes are discussed in detail.

From regular black holes to horizonless objects: quasi-normal modes, instabilities and spectroscopy

“…To understand the fine details, the interested reader can follow the full derivation of the perturbative equations in appendix A and in particular the comment in footnote 4. On the other hand, other authors have analyzed linear perturbations carefully, but specialized to non-linear electrodynamics without scalar fields or viceversa [36][37][38][39][40][41]. Our perturbative analysis extends these results to a generic spacetime described by the line element (2.1), interpreted as an exact solution of GR coupled to non-linear electrodynamics and scalar fields.…”

Gravito-electromagnetic perturbations of MOG black holes with a cosmological constant: quasinormal modes and ringdown waveforms

“…Inserting the harmonic expansion of the metric perturbation (3.2) and the vector perturbation (3.3) into the linearized field equations (2.8) and (2.10), one can obtain all components of the equations. In fact, there is no reason to consider that the axial and polar parts will not be automatically separated [38][39][40][41][42]. However, by separating the angular dependence [43], a system of fourteen coupled pure radial equations can be obtained.…”