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We apply the Gauss-Bonnet theorem to the study of light rays in a plasmamedium in a static and spherically symmetric gravitational field and also tothe study of timelike geodesics followed for test massive particles in aspacetime with the same symmetries. The possibility of using the theoremfollows from a correspondence between timelike curves followed by light rays ina plasma medium and spatial geodesics in an associated Riemannian opticalmetric. A similar correspondence follows for massive particles. For someexamples and applications, we compute the deflection angle in weakgravitational fields for different plasma density profiles and gravitationalfields.

Weak lensing in a plasma medium and gravitational deflection of massive particles using the Gauss-Bonnet theorem. A unified treatment