Gravitational lensing represents the deflection of waves propagating in the vicinity of massive astrophysical objects, such as black holes, stars or galaxies. The theoretical model generally used for describing gravitational lensing is the geometrical optics approximation, in which case waves are assumed to have infinite frequency and their propagation is described in terms of the geodesics of the underlying spacetime.

The aim of this project is to study the gravitational lensing of electromagnetic and gravitational waves by means of an improved theoretical model. By considering higher-order corrections to the geometrical optics approximation, at finite frequencies, the propagation of electromagnetic and gravitational waves becomes polarization dependent. This represents the gravitational spin Hall effect.

A numerical code will be developed for the integration of the polarization-dependent ray equations that describe the gravitational spin Hall effect. This will help us determine the size of this effect in various spacetimes of astrophysical interest. We will study the lensing of polarized electromagnetic and gravitational waves propagating near black holes. Furthermore, by investigating the regime of strong gravitational lensing, we will look for polarization-dependent corrections to the shape of black hole shadows.