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  • Open Access

Proper time observables of general gravitational perturbations in laser interferometry-based gravitational wave detectors

Vincent S. H. Lee1,2,3,* and Kathryn M. Zurek1,†

  • *Contact author: vincentszehimlee@berkeley.edu
  • †Contact author: kzurek@caltech.edu
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Phys. Rev. D 111, 124037 – Published 20 June, 2025

DOI: https://doi.org/10.1103/6q7d-jz26

Abstract

We present an explicitly gauge-invariant observable of any general gravitational perturbation, hμν [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.

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Outline

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Phys. Rev. D 111, 124037– Published 20 June, 2025
  • Received 30 August 2024
  • Revised 28 March 2025
  • Accepted 6 June 2025
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