Weak Gravitational Lensing in Ricci-Coupled Kalb-Ramond Bumblebee Gravity: Global Monopole and Axion-Plasmon Medium Effects

In this paper, we study the influence of the axion-plasmon medium, as proposed in [10.1103/PhysRevLett.120.181803]\cite{Tercas:2018gxv}, on the optical properties of black holes in a Lorentz-violating spacetime containing a global monopole. Our primary aim is to provide a test for detecting the effects of a fixed axion-plasmon background within the framework of Ricci-coupled Kalb-Ramond bumblebee gravity. By extending the conventional Einstein-bumblebee model through a nonminimal coupling between the Kalb-Ramond field and the Ricci tensor, we demonstrate that the combined presence of a global monopole and Lorentz-violating effects induces significant modifications to the classical Schwarzschild lensing signature. Employing the Gauss-Bonnet theorem within an optical geometry approach, we derive an analytical expression for the deflection angle that incorporates both linear and quadratic contributions from the Lorentz-violating parameter and the monopole charge. Furthermore, we investigate how the axion-plasmon coupling alters light propagation, affecting key observable gravitational deflection angle. Our results indicate that these optical characteristics are notably sensitive to the axion-plasmon parameters, thereby offering promising observational signatures for probing new physics beyond standard general relativity.