Spin Hall effect of Photons in a Static Gravitational Field

TL;DR

This paper derives semiclassical equations of motion for photons in static gravitational fields, revealing a gravitational birefringence effect caused by helicity-dependent deviations from null geodesics.

Contribution

It introduces a Hamiltonian-based semiclassical framework for photon propagation in gravity, uncovering a new helicity-magnetotorsion coupling and anomalous velocity effects.

Findings

Photons exhibit helicity-dependent geodesic deviations.

New helicity-magnetotorsion coupling identified.

Gravitational birefringence demonstrated.

Abstract

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 static gravitational field. These equations which are obtained in the representation diagonalizing the Hamiltonian at the order $\hbar $, present the first order corrections to the geometrical optics. The photon Hamiltonian shows a new kind of helicity-magnetotorsion 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.