Finite distance corrections to the light deflection in a gravitational field with a plasma medium

The aim of the present work is twofold: first, we present general remarks about the application of recent procedures to compute the deflection angle in spherically symmetric and asymptotically flat spacetimes, taking into account finite distance corrections based on the Gauss-Bonnet theorem. Second, and as the main part of our work, we apply this powerful technique to compute corrections to the deflection angle produced by astrophysical configurations in the weak gravitational regime when a plasma medium is taken into account. For applications, we use these methods to introduce new general formulas for the bending angle of light rays in plasma environments in different astrophysical scenarios, generalizing previously known results. We also present new and useful formulas for the separation angle between the images of two sources when they are lensed by an astrophysical object surrounded by plasma. In particular, for the case of a homogeneous plasma we study these corrections for the case of light rays propagating near astrophysical objects described in the weak gravitational regime by a parametrized-post-Newtonian metric which takes into account the mass of the objects and a possible quadrupole moment. Even when our work concentrates on finite distance corrections to the deflection angle, we also obtain as particular cases of our expressions new formulas which are valid for the more common assumption of infinite distance between receiver, lens and source. We also consider the presence of an inhomogeneous plasma media introducing as particular cases of our general results explicit expressions for particular charge number density profiles.