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.
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