  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 of special cases, but no general
description has been proposed. Here, we present a covariant
Wentzel-Kramers-Brillouin 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 reported here is analogous to that of the spin Hall effect of
light in inhomogeneous media, which has been experimentally verified.
