Geodesic deviation and gravitational waves

TL;DR

This paper analyzes how gravitational waves affect geodesic deviation, revealing that in the standard gauge, the effect is not directly observable through the equation, but it is in the detector's proper frame.

Contribution

It clarifies the gauge dependence of gravitational wave detection via geodesic deviation and emphasizes the importance of the proper Lorentz frame for observable effects.

Findings

In the traceless-transverse gauge, wave components do not influence geodesic deviation.

The measurable effect of gravitational waves appears only in the detector's proper Lorentz frame.

The coordinate-based geodesic deviation equation may not directly reflect physical observables.

Abstract

The detection of gravitational waves based on the geodesic deviation equation is discussed. In particular, it is shown that the only non-vanishing components of the wave field in the conventional traceless-transverse gauge in linearized general relativity do not enter the geodesic deviation equation, and therefore, apparently, no effect is predicted by that equation in that specific gauge. The reason is traced back to the fact that the geodesic deviation equation is written in terms of a coordinate distance, which is not a directly measurable quantity. On the other hand, in the proper Lorentz frame of the detector, the conventional result described in standard textbooks holds.