Thermodynamics, Shadow, and Quasinormal Modes of AdS Ay\'on--Beato--Garc\'ia Massive Black Hole

TL;DR

This paper explores the thermodynamics, photon sphere, shadow, and stability of an AdS Ayón--Beato--García massive black hole, revealing how graviton mass and magnetic charge influence its properties and stability.

Contribution

It provides a comprehensive analysis of how graviton mass and magnetic charge affect black hole thermodynamics, shadow, and quasinormal modes in modified gravity.

Findings

Gibbs free energy interpolates between different black hole solutions.

Increasing graviton mass expands the photon sphere and shadow radii.

Quasinormal modes confirm the black hole's dynamical stability.

Abstract

We investigate the thermodynamics, photon sphere, and dynamical stability of an AdS Ay\'{o}n--Beato--Garc\'{i}a (ABG) massive black hole with graviton mass and magnetic charge. The Gibbs free energy exhibits distinct limiting behaviors: it reduces to that of an AdS massive black hole when magnetic charge vanishes, to that of an AdS ABG black hole when graviton mass is zero, and smoothly interpolates to the AdS massive Reissner-Nordstr\"om case in the asymptotic regime. Furthermore, the photon sphere and shadow analysis indicate that increasing the graviton mass expands their radii, while increasing the magnetic charge causes contraction, in agreement with earlier studies of black hole spacetimes. Quasinormal mode (QNM) calculations further confirm dynamical stability, as the imaginary part remains negative, ensuring decay of perturbations. Additionally, the real part of the frequency decreases with graviton mass, while the imaginary part initially grows before saturating at higher values. Together, these results provide meaningful insights into the interplay between graviton mass, magnetic charge, and stability, thereby enriching the understanding of black holes in modified gravity theories.