Light bending and observational bounds in dyonic Kalb-Ramond gravity

Abstract

We investigate the weak and strong gravitational lensing of a dyonic black hole in Kalb-Ramond gravity. After fixing the asymptotic normalization, we distinguish the effective charge governing the local null trajectories from the global angular identification associated with Lorentz-symmetry breaking. In the weak-deflection regime, we evaluate the Gaussian curvature explicitly and apply the Gauss-Bonnet theorem with a perturbed ray boundary, recovering the complete second order mass contribution. Independent calculations based on the orbit equation, the turning point integral, and Fermat's principle reproduce the same bending angle. In the strong-deflection regime, Tsukamoto's method yields closed expressions for both strong-deflection coefficients, with exact charge dependence. We derive finite-distance lens equations and the associated image positions, magnifications, flux ratios, and differential arrival times, retaining the physical winding condition. Shadow sizes inferred from observations of Sgr~A$^*$ and M87$^*$ yield conditional charge bounds, complemented by an estimate from S2 precession. We further construct combinations of strong-lensing observables that separate the effective charge from the conical parameter within the model: angular separation and relative brightness remove the explicit winding dependence, while a timing ratio incorporating an independent distance estimate isolates the conical deformation.