  We apply the analogy between gravitational fields and optical media in the
general relativistic geometric optics framework to describe how light can
acquire orbital angular momentum (OAM) when it traverses the gravitational
field of a massive rotating compact object and the interplay between OAM and
polarization. Kerr spacetimes are known not only to impose a gravitational
Faraday rotation on the polarization of a light beam, but also to set a
characteristic fingerprint in the orbital angular momentum distribution of the
radiation passing nearby a rotating black hole (BH). Kerr spacetime behaves
like an inhomogeneous and anisotropic medium, in which light can acquire
orbital angular momentum and spin-to-orbital angular momentum conversion can
occur, acting as a polarization and phase changing medium for the
gravitationally lensed light, as confirmed by the data analysis of M87* black
hole.
