# Relaxations of perturbations of spacetimes in general relativity coupled to nonlinear electrodynamics

## TL;DR

This paper investigates the relaxation times of scalar, electromagnetic, and gravitational perturbations in regular black hole and no-horizon spacetimes within general relativity coupled to nonlinear electrodynamics, comparing them with classical solutions.

## Contribution

It provides the first analysis of perturbation relaxation times in NED-coupled GR regular spacetimes, highlighting their unique oscillation properties and potential observational signatures.

## Key findings

- Regular spacetimes in NED do not have vanishing circular photon orbits.
- Electromagnetic perturbations always oscillate with quasinormal frequencies.
- EM eikonal regime can reveal deviations from null geodesics and confirm Maxwellian weak field limits.

## Abstract

Three well known exact regular solutions of general relativity (GR) coupled to nonlinear electrodynamics (NED), namely the Maxwellian, Bardeen and Hayward regular spacetimes, which can describe either a regular black hole or a geometry without horizons, have been considered. Relaxation times for the scalar, electromagnetic (EM) and gravitational perturbations of black holes (BHs) and no-horizon spacetimes have been estimated in comparison with the ones of the Schwarzschild and Reissner-Nordstr\"{o}m (RN) spacetimes. It has been shown that the considered geometries in GR coupled to the NED have never vanishing circular photon orbits and on account of this fact these spacetimes always oscillate the EM perturbations with quasinormal frequencies (QNFs). Moreover we have shown that the EM perturbations in the eikonal regime can be a powerful tool to confirm that (i) the light rays do not follow null geodesics in the NED by the relaxation rates; (ii) if the underlying solution has a correct weak field limit to the Maxwell electrodynamics (LED) by the angular velocity of the circular photon orbit.