Spin Hall effect of photons in a static gravitational field

Starting from a Hamiltonian description of the photon within the set of Bargmann-Wigner equations we derive new semiclassical equations of motion for the photon propagating in a static gravitational field. These equations which are obtained in the representation diagonalizing the Hamiltonian at the order, present the first order corrections to the geometrical optics. The photon Hamiltonian shows a new kind of helicity-torsion coupling. However, even for a torsionless space-time, photons do not follow the usual null geodesic as a consequence of an anomalous velocity term. This term is responsible for the gravitational birefringence phenomenon: photons with distinct helicity follow different geodesics in a static gravitational field.