The propagation of electromagnetic waves in vacuum is often described within the geometrical optics approximation, which predicts that wave rays follow null geodesics. However, this model is valid only in the limit of infinitely high frequencies. At large but finite frequencies, diffraction can still be negligible, but the ray dynamics becomes affected by the evolution of the wave polarization. Hence, rays can deviate from null geodesics, which is known as the gravitational spin Hall effect of light. By considering the WKB approximation for Maxwell's equations, I will briefly present the main steps towards a covariant derivation of the polarization-dependent ray equations describing the gravitational spin Hall effect of light. Based on these equations, I will present some representative examples of polarized light rays in Schwarzschild and Kerr spacetimes, as well as some preliminary results about the effect on black hole shadows. Based on arXiv:2003.04553.

# The gravitational spin Hall effect of light

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