Photon polarization and geometric phase in general relativity

TL;DR

This paper investigates the rotation of photon polarization caused by gravitational fields in general relativity, introducing a new local reference frame and a novel expansion method to analyze the geometric phase effects.

Contribution

It introduces an operationally-motivated local reference frame and a new expansion parameter for null geodesics in Kerr space-time, enabling clearer analysis of polarization rotation and geometric phase.

Findings

Derived a gauge-independent geometric phase for closed paths.

Developed a simple description of polarization rotation using the new reference frame.

Provided a controlled series expansion for null geodesics in Kerr space-time.

Abstract

Rotation of polarization in an external gravitational field is one of the effects of general relativity that can serve as a basis for its precision tests. A careful analysis of reference frames is crucial for a proper evaluation of this effect. We introduce an operationally-motivated local reference frame that allows for a particularly simple description. We present a solution of null geodesics in Kerr space-time that is organized around a new expansion parameter, allowing a better control of the series, and use it to calculate the resulting polarization rotation. While this rotation depends on the reference-frame convention, we demonstrate a gauge-independent geometric phase for closed paths in general space-times.