Spin vector deviation and the gravitational wave memory effect between two free-falling gyroscopes in the plane wave spacetime

TL;DR

This paper investigates how gravitational waves in plane wave spacetime cause a measurable precession angle deviation between two free-falling gyroscopes, linked to the velocity memory effect, with potential detectability in future experiments.

Contribution

It introduces the concept of spin vector deviation as a gravitational wave memory effect in plane wave spacetime, providing calculations for different initial conditions and potential observability.

Findings

Angle deviation can reach 10^{-14} radians for binary sources.

Deviation depends on initial separation velocity and displacement.

Memory effect may be detectable in future gravitational wave observations.

Abstract

In the plane wave spacetime, we find that there will be a precession angle deviation between two free-falling gyroscopes when gravitational waves passed through. This kind of angle deviation is closely related to the well-known standard velocity memory effect. Initial conditions such as the separation velocity or displacement between the two gyroscopes will affect this angle deviation. The evolutions of the angle deviation are calculated for different cases. We find that in some extreme circumstance, the angle deviation's order of magnitude produced by a rotating compact binary source could be $10^{-14}$ rads. Therefore, this memory effect caused by the gravitational wave is likely to be detected in the future.