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Abstract

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. In the literature, this effect has
been calculated ad hoc for a number for special cases, but no general
description has been proposed. Here, we present a covariant WKB analysis from
first principles for the propagation of light in arbitrary curved spacetimes.
We obtain polarization-dependent ray equations describing the gravitational
spin Hall effect of light. We also present numerical examples of
polarization-dependent ray dynamics in the Schwarzschild spacetime, and the
magnitude of the effect is briefly discussed. The analysis presented here is
analogous to the spin Hall effect of light in inhomogeneous media, which has
been experimentally verified.