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We apply the analogy between gravitational fields and optical media in thegeneral relativistic geometric optics framework to describe how light canacquire orbital angular momentum (OAM) when it traverses the gravitationalfield of a massive rotating compact object and the interplay between OAM andpolarization. Kerr spacetimes are known not only to impose a gravitationalFaraday rotation on the polarization of a light beam, but also to set acharacteristic fingerprint in the orbital angular momentum distribution of theradiation passing nearby a rotating black hole (BH). Kerr spacetime behaveslike an inhomogeneous and anisotropic medium, in which light can acquireorbital angular momentum and spin-to-orbital angular momentum conversion canoccur, acting as a polarization and phase changing medium for thegravitationally lensed light, as confirmed by the data analysis of M87* blackhole.

Kerr spacetime geometric optics for vortex beams