Thermodynamics, Shadow, and Quasinormal Modes of AdS Ayón--Beato--García Massive Black Hole

Abstract

We investigate the thermodynamics, photon sphere, and dynamical stability of an AdS Ayón--Beato--García (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-Nordström 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.

Figures (12)

• Figure 1: The plot illustrates the function $f(r)$ as a function of the radial coordinate $r$. The upper panel presents $f(r)$ for varying values of the graviton mass while keeping the magnetic charge $g$ fixed. Conversely, the lower panel depicts $f(r)$ for different values of the magnetic charge $g$ with a fixed graviton mass.
• Figure 2: The plot of the metric function against the radial distance with the limiting values of $m$ and $g$.
• Figure 3: The upper panel illustrates the relationship between temperature and horizon radius for various values of graviton mass, while the lower panel shows the temperature vs. horizon radius for different values of magnetic charge, with the graviton mass held constant.
• Figure 4: The Plot of the temperature against the horizon radius with the limiting values of $m$, $g$ and $m,g$.
• Figure 5: Plot of heat capacity versus horizon radius: The upper panel shows variations for different values of graviton mass with a fixed magnetic charge, while the lower panel depicts variations for different values of magnetic charge with a fixed graviton mass.