  The purpose of this article is twofold. First, we extend the results
presented in [Gabriel Crisnejo and Emanuel Gallo, Phys.Rev.D 97, 124016 (2018)]
to stationary spacetimes. Specifically, we show that the Gauss-Bonnet theorem
can be applied to describe the deflection angle of light rays in plasma media
in stationary spacetimes. Second, by using a correspondence between the motion
of light rays in a cold non magnetized plasma and relativistic test massive
particles we show that this technique is not only powerful to obtain the
leading order behavior of the deflection angle of massive/massless particles in
the weak field regime but also to obtain higher order corrections. We
particularize it to a Kerr background where we compute the deflection angle for
test massive particles and light rays propagating in a non homogeneous cold
plasma by including third order corrections in the mass and spin parameters of
the black hole.
