Proper Time Observables of General Gravitational Perturbations in Laser Interferometry-based Gravitational Wave Detectors

TL;DR

This paper introduces a gauge-invariant proper time observable for gravitational perturbations in laser interferometry detectors, unifying the treatment of gravitational waves and other spacetime fluctuations.

Contribution

It presents a new gauge-invariant formalism for measuring gravitational perturbations via proper time in interferometers, applicable to various signals beyond standard gravitational waves.

Findings

Proper time observable matches the detector strain for plane GWs

The formalism is invariant under diffeomorphisms

Applicable to signals like dark matter and quantum gravity fluctuations

Abstract

We present an explicitly gauge-invariant observable of {\em any} general gravitational perturbation, $h_{\mu\nu}$ (\textit{not} necessarily due to gravitational waves (GWs)), in a laser interferometry-based GW detector, identifying the signature as the proper time elapsed of the beamsplitter observer, between two events: when a photon passes through the beamsplitter, and when the same photon returns to the beamsplitter after traveling through the interferometer arm and reflecting off the far mirror. Our formalism applies to simple Michelson interferometers and can be generalized to more advanced setups. We demonstrate that the proper time observable for a plane GW is equivalent to the detector strain commonly used by the GW community, though now the common framework can be easily generalized for other types of signals, such as dark matter clumps or spacetime fluctuations from quantum gravity. We provide a simple recipe for computing the proper time observable for a general metric perturbation in linearized gravity and explicitly show that it is invariant under diffeomorphisms of the perturbation, as any physical observable should be.