The Response of Test Masses to Gravitational Waves in the Coordinates of a Local Observer

TL;DR

This paper clarifies how gravitational waves affect test masses in local observer coordinates, resolving discrepancies with other gauges and demonstrating the invariance of the response function across different coordinate systems.

Contribution

It provides a comprehensive analysis of test mass responses in local coordinates, unifying different calculation methods and confirming their consistency for large separations.

Findings

Response includes mass displacement, photon velocity change, and clock variation effects.

The combined effects form a translationally invariant response function.

Results are valid for large test mass separations.

Abstract

The response of laser interferometers to gravitational waves has been calculated in a number of different ways, particularly in the transverse-traceless and the local Lorentz gauges. At first sight, it would appear that these calculations lead to different results when the separation between the test masses becomes comparable to the wavelength of the gravitational wave. In this paper this discrepancy is resolved. We describe the response of free test masses to plane gravitational waves in the coordinate frame of a local observer and show that it acquires contributions from three different effects: the displacement of the test masses, the apparent change in the photon velocity, and the variation in the clock speed of the local observer, all of which are induced by the gravitational wave. Only when taken together do these three effects represent a quantity which is translationally invariant. This translationally-invariant quantity is identical to the response function calculated in the transverse-traceless gauge. We thus resolve the well-known discrepancy between the two coordinates systems, and show that the results found in the coordinate frame of a local observer are valid for large separation between the masses.