Chromatic Weak Lensing by Charged Black Holes with Two Lorentz-Violating Kalb-Ramond Couplings

Abstract

We study weak gravitational lensing and steady spherical test--fluid accretion by a static charged black hole in a Lorentz--violating Kalb--Ramond background with two nonminimal curvature couplings, assuming minimally coupled probe radiation. Using the Gauss--Bonnet theorem with the correct boundary term and perturbed ray boundary, we obtain the complete local deflection angle through second post--Minkowskian order. In a homogeneous cold plasma, the mass and charge sectors acquire different frequency dependences, producing distinct chromatic signatures. The two Lorentz--violating couplings are also separated: one controls the conical geometry and mass normalization, while the other first enters through the effective charge. For neutral adiabatic accretion, we derive the conserved fluxes, Bernoulli relation, Hamiltonian flow, and sonic--point conditions. These results disentangle local, global, dispersive, and accretion effects and establish the calibrations required for phenomenological constraints.