An Exact Expression for Photon Polarization in Kerr Geometry

TL;DR

This paper derives a precise, coordinate-independent formula for how photon polarization rotates when traveling along null geodesics in Kerr spacetime, aiding quantum communication analysis.

Contribution

It provides a closed-form, intrinsic expression for photon polarization transport in Kerr geometry using Killing-Yano theory, improving upon previous complex methods.

Findings

The polarization rotation formula is compact and explicit.

The phase vanishes on the equatorial plane and symmetry axis.

The method is applicable to arbitrary null geodesics in Kerr spacetime.

Abstract

We analyze the transformation of the polarization of a photon propagating along an arbitrary null geodesic in Kerr geometry. The motivation comes from the problem of an observer trying to communicate quantum information to another observer in Kerr spacetime by transmitting polarized photons. It is essential that the observers understand the relationship between their frames of reference and also know how the photon's polarization transforms as it travels through Kerr spacetime. Existing methods to calculate the rotation of the photon polarization (Faraday rotation) depend on choices of coordinate systems, are algebraically complex and yield results only in the weak-field limit. We give a closed-form expression for a parallel propagated frame along an arbitrary null geodesic using Killing-Yano theory, and thereby solve the problem of parallel transport of the polarization vector in an intrinsic, geometrically-motivated fashion. The symmetries of Kerr geometry are utilized to obtain a remarkably compact expression for the geometrically induced phase of the photon's polarization. We show that this phase vanishes on the equatorial plane and the axis of symmetry.