Exploring Lorentz-violating effects of Kalb-Ramond field on charged black hole thermodynamics and photon dynamics

This study explores the influence of the Kalb-Ramond (KR) field, characterized by Lorentz-violating effects, on the structure, thermodynamics, and observational phenomena of Reissner-Nordstr"om-like black holes. By introducing a modified Einstein-Hilbert action incorporating the KR field's nonminimal coupling with the \ifmmode \bar{\imath}\else \={\i}\fi{}Ricci tensor, we derive a spherically symmetric black hole solution. The Lorentz-violating parameter $L$ alters the black hole's horizon structure, curvature invariants, and thermodynamic properties, such as Hawking temperature and entropy, with exponential quantum corrections offering deeper insights into high-energy phenomena. Photon dynamics in both vacuum and plasma environments reveal refractive effects due to the KR field, with weak gravitational lensing analyzed using the Gauss-Bonnet theorem and perturbative methods, including higher-order deflection corrections. Observational signatures like modified photon spheres, lensing angles, and shadows are discussed, providing potential avenues for experimental validation.