Charged Black Holes in Bumblebee gravity with Global Monopole: Thermodynamics and Shadow

Abstract

In this paper, we perform a detailed study of the thermodynamic properties of a charged black hole in bumblebee gravity in the presence of a global monopole. We also analyze the optical characteristics of this black hole solution, highlighting the influence of Lorentz symmetry violation and the global monopole on the black hole shadow. Furthermore, we examine the trajectories of both photons and test particles in this spacetime, showing how the geometric parameters alter their paths. Moreover, we study the dynamics of neutral test particles, with particular attention to the location of the innermost stable circular orbits (ISCOs). Finally, we investigate massless scalar perturbations and derive bounds on the greybody factors, illustrating how the black hole's geometric parameters affect field propagation, energy emission, and radiation sparsity in this background.

Figures (20)

• Figure 1: Metric function $f(r)$ versus the radial coordinate $r$ for fixed charge $Q=0.8$. Panel (a) shows the effect of varying the Lorentz-violating parameter $\ell$ at fixed monopole parameter $\eta=0.3$, while panel (b) shows the effect of varying $\eta$ at fixed $\ell=0.2$. The zeros of each curve correspond to the inner and outer horizons.
• Figure 2: Hawking temperature $T_H$ as a function of the horizon radius $r_h$ for fixed $Q=0.8$. Panel (a) shows the dependence on $\ell$ at fixed $\eta=0.3$, while panel (b) shows the dependence on $\eta$ at fixed $\ell=0.2$. The curves display the typical non-monotonic behavior of charged black holes, with a maximum separating different thermal regimes.
• Figure 3: ADM mass $M$ as a function of the horizon radius $r_h$ for fixed $Q=0.8$. Panel (a) corresponds to $\eta=0.3$ with varying $\ell$, and panel (b) corresponds to $\ell=0.2$ with varying $\eta$. The curves show how the mass--radius relation is deformed by Lorentz violation and the monopole background.
• Figure 4: Gibbs free energy $G$ as a function of the horizon radius $r_h$ for fixed $Q=0.8$. Panel (a) shows varying $\ell$ at fixed $\eta=0.3$, while panel (b) shows varying $\eta$ at fixed $\ell=0.2$. The monotonic behavior indicates how the thermodynamic potential shifts with the geometric parameters.
• Figure 5: Specific heat at constant charge, $C_Q$, as a function of the horizon radius $r_h$ for fixed $Q=0.8$. Panel (a) corresponds to $\eta=0.3$ with varying $\ell$, and panel (b) corresponds to $\ell=0.2$ with varying $\eta$. The divergence marks the transition between locally stable ($C_Q>0$) and unstable ($C_Q<0$) branches.