Spinoptics in a stationary spacetime

TL;DR

This paper investigates how photon polarization influences their trajectories in a stationary gravitational field, revealing modifications to standard geometrical optics due to helicity effects, especially in the late-time regime.

Contribution

It introduces a modified geometrical optics approach that accounts for photon helicity, providing new equations for polarized light propagation in curved spacetime, specifically in Kerr geometry.

Findings

Helicity affects photon trajectories in stationary spacetimes.

Modified equations incorporate a small correction proportional to inverse frequency.

Late-time behavior of polarized beams differs from standard geometrical optics.

Abstract

The main goal of the present paper is to study how polarization of photons affects their motion in a gravitational field created by a rotating massive compact object. We study propagation of the circularly polarized beams of light in a stationary gravitational field. We use (3+1)-form of the Maxwell equations to derive a master equation for the propagation of monochromatic electromagnetic waves of the frequency $\omega$ with a given helicity. We first analize its solutions in the high frequency approximation using the `standard' geometrical optics approach. After that we demonstrate how this `standard' approach can be modified in order to include the effect of the helicity of photons on their motion. Such an improved method reproduces the standard results of the geometrical optics at short distances. However, it modifies the asymptotic behavior of the circularly polarized beams in the late-time regime. We demonstrate that the corresponding equations for the circularly polarized beam can be effectively obtained by modification of the background geometry by including a small factor proportional to $\omega^{-1}$ whose sign corresponds to photon helicity. We obtain the modified equations for circularly polarized rays by using such a `renormalization' procedure, and calculate the corresponding renormalization term for the Kerr geometry.