Photon spheres, gravitational lensing/mirroring, and greybody radiation in deformed AdS-Schwarzschild black holes with phantom global monopole

TL;DR

The paper investigates how a deformed AdS-Schwarzschild black hole with global monopoles—ordinary or phantom—modifies geodesic structure, gravitational lensing, and scalar perturbations. By introducing a metric with deformation $α$ and regulator $β$, along with symmetry-breaking scale $η$, the authors compute photon-sphere radii, Lyapunov exponents, deflection angles via Gauss–Bonnet, and greybody factors from the Klein–Gordon equation, employing Visser bounds. A striking result is the gravitational mirroring effect: phantom GM can produce negative deflection angles at large AdS curvature, while ordinary GM enhances gravitational attraction, with deformation further tuning these effects. The study provides multiple observational signatures—shadows, lensing patterns, and Hawking radiation spectra—that could help detect phantom topological defects and test modified gravity in AdS-like spacetimes.

Abstract

In this study, we investigate the geodesic structure, gravitational lensing/mirroring phenomena, and scalar perturbations of deformed AdS-Schwarzschild black holes with global monopoles, incorporating both ordinary and phantom configurations. We introduce a modified black hole metric characterized by a deformation parameter $α$, a control parameter $β$, and a symmetry-breaking scale parameter $η$, which collectively influence the spacetime geometry. Through comprehensive geodesic analysis, we determine the photon sphere radius numerically for various parameter configurations, revealing significant differences between ordinary and phantom global monopoles. The stability of timelike circular orbits is assessed via the Lyapunov exponent, demonstrating how these parameters affect orbital dynamics. Our gravitational lensing analysis, employing the Gauss-Bonnet theorem, reveals a remarkable gravitational mirroring effect in phantom monopole spacetimes at high AdS curvature radii, where light rays experience negative deflection angles-being repelled rather than attracted by the gravitational field. Furthermore, we analyze massless scalar perturbations and derive the corresponding greybody factors, which characterize the transmission of Hawking radiation through the effective potential barrier surrounding the black hole. Our numerical results indicate that phantom global monopoles substantially modify both gravitational lensing/mirroring properties and the radiation spectrum compared to ordinary monopoles. The presence of the deformation parameter $α$ introduces additional complexity to the system, leading to distinct thermodynamic behavior that deviates significantly from the standard AdS-Schwarzschild solution.

Figures (7)

• Figure 1: The profile of the photon sphere radius for various values of BH parameters $\alpha$ and $\beta$ for fixed $\eta=0.6$ showing that the $r_{ph}$ has higher value for ordinary GMs than phantom GMs. Here, $M=1$.
• Figure 2: The profile of the photon sphere radius for various values of BH parameters $\alpha$ and $\beta$ for fixed $\eta=0.6$ showing that the $r_{ph}$ decreases with $\alpha$ but increases with $\beta$. Here, $M=1$.
• Figure 3: The profile of the ISCO for various values of BH parameters $\alpha$ and $\beta$ for fixed $\eta=0.4$ showing that the $r_{ISCO}$ has higher value for phantom GMs than ordinary GMs. Here $M=1$.
• Figure 4: The profile of the ISCO for various values of BH parameters $\alpha$ and $\beta$ for fixed $\eta=0.4$ showing that the $r_{ISCO}$ decreases with $\alpha$ but increases with $\beta$. Here, $M=1$.
• Figure 5: The profile of the deflection angle $\tilde{\Delta}$ around the deformed AdS-Schwarzschild BH with phantom GMs as a function of the impact parameter $b$ for varying values of the deformation parameter $\alpha$ with low AdS curvature radius $\ell_p=0.1$ [see panel (a)] and with high AdS curvature radius $\ell_p=2$ [see panel b)]. The fixed parameters are chosen as $M=\beta=1$, $\xi=-1$, and $\eta = 0.5$.