Strong Gravitational Lensing by a Black Hole with a Global Monopole in Kalb-Ramond Bumblebee Gravity

TL;DR

The paper investigates strong gravitational lensing and black hole shadows in a static black hole spacetime sourced by a global monopole within Ricci-coupled Kalb-Ramond Bumblebee gravity, characterized by the monopole charge $\kappa\eta^2$ and Lorentz-violating parameter $\gamma$. By deriving the modified metric, horizon, and photon-sphere properties, the authors compute the strong deflection limit coefficients $C^{(1)}$ and $C^{(2)}$ and translate them into observables such as relativistic Einstein rings, magnifications, limiting angular radius $\theta_{\infty}$, image separations, and flux ratios for Sgr A$^*$ and M87$^*$; they show how $\kappa\eta^2$ and $\gamma$ shift these observables. They extend the analysis to shadow formation both in vacuum and with an optically thin radially infalling accretion flow, finding that the shadow size increases with $\kappa\eta^2$ and decreases with $\gamma$, with accretion effects amplifying or damping brightness near the shadow boundary accordingly. The study provides observational signatures that could test global monopole and Lorentz-violating gravity in the strong-field regime with current or future very-long-baseline interferometry, and suggests further work on rotating BHs and massive-particle lensing as future tests.

Abstract

We investigate the strong gravitational lensing and shadow properties of the black hole in the context of bumblebee gravity, characterized by a global monopole charge $κη^2$ and a Lorentz symmetry breaking parameter $γ$. We compute the deflection angles of light passing near the black hole in strong deflection limit, and estimate key lensing observables, including relativistic Einstein rings, absolute magnifications, image separations, and flux ratios, for astrophysical black holes. The black hole shadow is analyzed using the apparent angular size $θ_{\rm Shadow} = 2\,θ_{\infty}$ in the limiting photon orbit. Furthermore, we study the modification of the shadow structure in the presence of a radially infalling, optically thin accretion flow within a generalized framework. Our results indicate that both the global monopole charge and Lorentz-violating parameters significantly influence the photon sphere, lensing observables, and shadow morphology, potentially providing observational signatures for testing bumblebee gravity in the strong-field regime.

Figures (16)

• Figure 1: The plot of event horizon, versus BH parameter $\gamma$ (left) and $\kappa\eta^{2}$ (right)
• Figure 2: Effective potential at fixed value of $\gamma=0.1,\kappa\eta^2=0.1$ (left). In right plot $\gamma=0.1,u=2.608$. Equal values of BH parameter correspond to Schwarzschild BH, denoted by subscript (S).
• Figure 3: The plot of photon radius,versus BH parameter $\gamma$ (left) and $\kappa\eta^{2}$ respectively (right)
• Figure 4: Plot of impact parameter for versus $\gamma$ (left) and $\kappa\eta^2$ (right) respectively.
• Figure 5: Schematic diagram of strong gravitational lensing.