The role of Wigner rotation in estimating the specific angular momentum of a Kerr spacetime

TL;DR

This paper investigates how gravitational polarization rotation in Kerr spacetime affects interferometric measurements, proposing a method to estimate the spacetime's angular momentum using a geodesic interferometer.

Contribution

It introduces a novel interferometric approach to estimate Kerr spacetime's angular momentum via polarization rotation effects in a geodesic interferometer.

Findings

Detection probability depends on gravitational time delay and polarization rotation.

Interferometric visibility encodes relativistic effects.

Method provides an estimate and uncertainty for the specific angular momentum.

Abstract

We study the rotation of the polarization due to the gravitational field in the Kerr spacetime and the possibility of estimating the specific angular momentum that parameterizes this metric. Our approach is based on a geodesic interferometer, that is, a Mach-Zehnder interferometer whose arms are defined by null geodesics, and a single photon propagating within it. We show that the detection probability at the output ports of the interferometer is a function of two phase differences, one arising from the gravitational time delay and the other from the polarization rotation, both computed under the slow rotation and weak field approximations. Thereby, the interferometric visibility is a signature of two relativistic effects. Using the detection probability, we obtain an estimate for the specific angular momentum and characterize its uncertainty.