The response of interferometric gravitational wave detectors

TL;DR

This paper critically examines the standard derivation of interferometric gravitational wave detector responses, identifies fundamental errors, and provides a corrected, detailed derivation to ensure accurate modeling of detector responses.

Contribution

It offers a rigorous correction to the traditional response function derivation, clarifying assumptions and conditions for accuracy in gravitational wave detection models.

Findings

Identified flaws in the standard derivation of detector response.

Provided a detailed, correct derivation of the response function.

Showed conditions where the standard derivation remains valid.

Abstract

The derivation of the response function of an interferometric gravitational wave detector is a paradigmatic calculation in the field of gravitational wave detection. Surprisingly, the standard derivation of the response wave detectors makes several unjustifiable assumptions, both conceptual and quantitative, regarding the coordinate trajectory and coordinate velocity of the null geodesic the light travels along. These errors, which appear to have remained unrecognized for at least 35 years, render the "standard" derivation inadequate and misleading as an archetype calculation. Here we identify the flaws in the existing derivation and provide, in full detail, a correct derivation of the response of a single-bounce Michelson interferometer to gravitational waves, following a procedure that will always yield correct results; compare it to the "standard", but incorrect, derivation; show where the earlier mistakes were made; and identify the general conditions under which the "standard" derivation will yield correct results. By a fortuitous set of circumstances, not generally so, the final result is the same in the case of Minkowski background spacetime, synchronous coordinates, transverse-traceless gauge metric perturbations, and arm mirrors at coordinate rest.