A note on the description of plane gravitational waves in Fermi coordinates

TL;DR

This paper uses Fermi coordinates to analyze plane gravitational waves, highlighting a gravitoelectromagnetic analogy and examining their effects on time measurements and local spacetime metrics.

Contribution

It introduces a gravitoelectromagnetic framework in Fermi coordinates to describe gravitational wave interactions and computes the local metric relevant for helicity-rotation coupling.

Findings

Wave effects on test masses described by Lorentz-like force

Order of magnitude of time measurement effects evaluated

Local spacetime metric expressed in cylindrical coordinates

Abstract

We use the formalism of Fermi coordinates to describe the interaction of a plane gravitational wave in the proper detector frame. In doing so, we emphasize that in this frame the action of the gravitational wave can be explained in terms of a gravitoelectromagnetic analogy. In particular, up to linear displacements from the reference world-line, the effects of the wave on test masses can be described in terms of a Lorentz-like force equation. In this framework we focus on the effects on time measurements provoked by the passage of the wave, and evaluate their order of magnitude. Eventually, we calculate the expression of the local spacetime metric in cylindrical coordinates adapted to the symmetries of the gravitational field and show its relevance in connection with the helicity-rotation coupling.