Gravitational Faraday and Spin-Hall Effects of Light

TL;DR

This paper investigates gravitational Faraday and spin-Hall effects of light in dynamic, asymptotically flat space-times, revealing how light polarization interacts with space-time angular momentum to produce observable polarization splitting and gravitational rainbow.

Contribution

It extends the study of these effects to non-stationary space-times and derives a dynamical equation describing polarization-dependent light propagation in such backgrounds.

Findings

Different phase velocities for left- and right-handed circular polarization.

Polarized gravitational rainbow caused by component separation.

Analogy between light propagation in gravitational field and charged particle in magnetic field.

Abstract

The gravitational Faraday and its dual spin-Hall effects of light arise in space-times of non-zero angular momentum. These effects were studied in stationary, asymptotically flat space-times. Here we study these effects in arbitrary, non-stationary, asymptotically flat space-times. These effects arise due to interaction between light polarisation and space-time angular momentum. As a result of such interaction, the phase velocity of left- and right-handed circularly polarised light becomes different, that results in the gravitational Faraday effect. This difference implies different dynamics of these components, that begin to propagate along different paths\textemdash the gravitational spin-Hall effect of light. Due to this effect, the gravitational field splits a multicomponent beam of unpolarized light and produces polarized gravitational rainbow. The component separation is an accumulative effect observed in long range asymptotics. To study this effect, we construct uniform eikonal expansion and derive dynamical equation describing this effect. To analyse the dynamical equation, we present it in the local space and time decomposition form. The spatial part of the equation presented in the related optical metric is analogous to the dynamical equation of a charged particle moving in magnetic field under influence of the Coriolis force.