Generalized gauge-invariance for gravitational waves

TL;DR

This paper demonstrates the gauge-invariance of interferometer responses to gravitational waves across different gauges, including full angular and frequency dependences, clarifying misconceptions and extending previous low-frequency or simplified geometry analyses.

Contribution

It provides a comprehensive proof of gauge-invariance for gravitational wave responses in realistic conditions, beyond previous low-frequency or simplified models.

Findings

Gauge-invariance holds in full angular and frequency ranges.

Clarification of misconceptions about interferometer response calculations.

Extension of previous results to more general geometries.

Abstract

The aim of this paper is to show the gauge-invariance on the response of interferometers to gravitational waves (GWs). In this process, after a review of results on the Tranverse-Traceless (TT) gauge, where, in general, the theoretical computations on GWs are performed, which is due for completness, we analyse the gauge of the local observer, which represents the gauge of a laboratory environment on Earth. The gauge-invariance between the two gauges is shown in its full angular and frequency dependences. In previous works in the literature this gauge-invariance was shown only in the low frequencies approximation or in the simplest geometry of the interferometer in respect to the propagating GW (i.e. both of the arms of the interferometer are perpendicular to the propagating GW). As far as the computation of the response functions in the gauge of the local observer is concerned, a common misconception about interferometers is also clarifed.