Gravitational Holonomy in Sagnac Interferometry

TL;DR

This paper investigates how gravitational waves affect Sagnac interferometers, revealing a new polarization rotation effect linked to gravitational holonomy, especially significant for freely falling observers.

Contribution

It introduces the concept of gravitational holonomy in Sagnac interferometry and quantifies polarization rotation effects caused by gravitational waves.

Findings

Polarization rotation dominates phase shift for freely falling observers.

Both effects are computed for gravitational waves from distant sources.

The study links gravitational holonomy to measurable interferometer signals.

Abstract

We analyze the influence of gravitational waves on a Sagnac interferometer formed by the interference of two counter-propagating beams traversing a closed spatial loop. In addition to the well-known Sagnac phase shift, we identify an additional contribution originating from a relative rotation in the polarization vectors. We formulate this effect as a gravitational holonomy associated to the internal Lorentz group. The magnitude of both effects is computed due to gravitational waves generated by a localized source far from the detector, at leading order in the inverse distance. For freely falling observers, the phase shift is zero and the polarization rotation becomes the dominant effect.