We consider the analogy between gravitational fields and optical media within the framework of geometrical optics in curved spacetime in order to describe how light can acquire orbital angular momentum (OAM) when it traverses the gravitational field of a massive rotating compact object; in particular, we analyze 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 the M87* black hole.

中文翻译：

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涡旋光束的克尔时空几何光学

我们在弯曲时空中的几何光学框架内考虑引力场和光学介质之间的类比，以描述光在穿过巨大旋转致密物体的引力场时如何获得轨道角动量（OAM）；我们特别分析了 OAM 和极化之间的相互作用。众所周知，克尔时空不仅对光束的偏振施加了引力法拉第旋转，而且还在通过旋转黑洞 (BH) 附近的辐射的轨道角动量分布中设置了特征指纹。克尔时空表现得像一种非均匀和各向异性的介质，其中光可以获得轨道角动量，并且可以发生自旋到轨道角动量的转换，