Gravitational Waves and the Sagnac Effect

TL;DR

This paper analyzes how gravitational waves influence the Sagnac effect, concluding that long-wavelength gravitational waves do not induce a measurable Sagnac effect in a closed light path.

Contribution

It provides a theoretical analysis showing that weak, long-wavelength gravitational waves do not produce a Sagnac effect, clarifying their impact on light propagation in general relativity.

Findings

Long-wavelength gravitational waves do not induce a Sagnac effect.

The Sagnac effect depends on the wave's wavelength relative to the light path.

Gravitational wave incident at any angle does not produce a measurable effect.

Abstract

We consider light waves propagating clockwise and other light waves propagating counterclockwise around a closed path in a plane (theoretically with the help of stationary mirrors). The time difference between the two light propagating path orientations constitutes the Sagnac effect. The general relativistic expression for the Sagnac effect is discussed. It is shown that a gravitational wave incident to the light beams at an arbitrary angle will not induce a Sagnac effect so long as the wave length of the weak gravitational wave is long on the length scale of the closed light beam paths. The gravitational wave induced Sagnac effect is thereby null.