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In this work we extend the approach used in [Emanuel Gallo and Osvaldo M.Moreschi, Phys. Rev. D 83, 12 083007 (2011)] to the study of weak gravitationallensing in a plasma medium. First, we present expressions for the deflectionangle and optical scalars in terms of the components of the energy-momentumtensor for spherically symmetric lenses surrounded by a cold non-magnetizedplasma. Second, we show that the same expressions can be deduced using theGauss-Bonnet theorem. Finally, we establish a correspondence between thespatial orbits of photons in a non-homogeneous plasma and the non-geodesiccurves followed by test massive particles whose dynamics also depend on anexternal central field. As an application, we use the Gauss-Bonnet theorem tocompute the deflection angle of the non-geodesic trajectories followed byrelativistic test massive charged particles in a Reissner-Nordstr\"omspacetime.

Gravitational lensing in dispersive media and deflection angle of charged massive particles in terms of curvature scalars and energy-momentum tensor