Alternative derivation of the response of interferometric gravitational wave detectors

TL;DR

This paper presents an alternative, simplified derivation of the response of interferometric gravitational wave detectors, addressing previous errors and offering a pedagogical approach by adapting methods from spacecraft Doppler tracking and pulsar timing.

Contribution

It introduces a new derivation method that avoids known errors and simplifies understanding of gravitational wave detector responses.

Findings

Provides a corrected derivation of interferometer response

Adapts spacecraft Doppler tracking and pulsar timing methods

Offers a pedagogical, simplified derivation

Abstract

It has recently been pointed out by Finn that the long-standing derivation of the response of an interferometric gravitational wave detector contains several errors. Here I point out that a contemporaneous derivation of the gravitational wave response for spacecraft doppler tracking and pulsar timing avoids these pitfalls, and when adapted to describe interferometers, recovers a simplified version of Finn's derivation. This simplified derivation may be useful for pedagogical purposes.