Quasinormal modes and shadows of a new family of Ay\'{o}n-Beato-Garc\'{\i}a black holes

TL;DR

This paper introduces a new family of Ayón-Beato-García black holes characterized by three parameters, analyzing their horizons, temperatures, quasinormal modes, and shadows, and comparing these with observational data from the M87* black hole.

Contribution

The study constructs a specific family of regular ABG black holes with three parameters and investigates their physical properties and observational signatures, including quasinormal modes and shadows.

Findings

The black holes are regular under certain parameter conditions.

The charge upper limit increases with the parameter rac{}{+} and does not exceed the black hole mass.

Shadow and quasinormal mode data constrain the black hole parameters and frequencies.

Abstract

We obtain a type of Ay\'{o}n-Beato-Garc\'{\i}a (ABG) related black hole solutions with five parameters: the mass $m$, the charge $q$, and three dimensionless parameters $\alpha$, $\beta$ and $\gamma$ associated with nonlinear electrodynamics. We find that this type of black holes is regular under the conditions: $\alpha \gamma \geqslant 6$, $\beta \gamma \geqslant 8$, and $\gamma >0$. Here we focus on the saturated case: $\alpha={6}/{\gamma}$ and $\beta ={8}/{\gamma }$, such that only three parameters $m$, $q$ and $\gamma$ remain, which leads to a new family of ABG black holes. For such a family of black holes, we investigate the influence of the charge $q$ and the parameter $\gamma$ on the horizon radius and the Hawking temperature. In addition, we calculate the quasinormal mode frequencies of massless scalar field perturbations by using the sixth-order WKB approximation method and the unstable circular null geodesic method in the eikonal limit. We also compute the shadow radius for the new family of ABG black holes and use the shadow data of the $M87^{*}$ black hole detected by the Event Horizon Telescope to provide an upper limit on the charge $q$ of the new black holes. Using the shadow data of the $M87^{*}$ black hole, we find that the upper limit of the charge $q$ increases rapidly at first and then slowly but does not exceed the mass of the $M87^{*}$ black hole at last when the parameter $\gamma$ is increasing and going to infinity, and that the data restrict the frequency range of the fundamental mode with $l=1$ to $1.4\times 10^{-6}Hz\sim 1.9\times 10^{-6} Hz$.