Gravitational wave detector response in terms of spacetime Riemann curvature

Abstract

Gravitational wave detectors are typically described as responding to gravitational wave metric perturbations, which are gauge-dependent and --- correspondingly --- unphysical quantities. This is particularly true for ground-based interferometric detectors, like LIGO, space-based detectors, like LISA and its derivatives, spacecraft doppler tracking detectors, and pulsar timing arrays detectors. The description of gravitational waves, and a gravitational wave detector's response, to the unphysical metric perturbation has lead to a proliferation of false analogies and descriptions regarding how these detectors function, and true misunderstandings of the physical character of gravitational waves. Here we provide a fully physical and gauge invariant description of the response of a wide class of gravitational wave detectors in terms of the Riemann curvature, the physical quantity that describes gravitational phenomena in general relativity. In the limit of high frequency gravitational waves, the Riemann curvature separates into two independent gauge invariant quantities: a "background" curvature contribution and a "wave" curvature contribution. In this limit the gravitational wave contribution to the detector response reduces to an integral of the gravitational wave contribution of the curvature along the unperturbed photon path between components of the detector. The description presented here provides an unambiguous physical description of what a gravitational wave detector measures and how it operates, a simple means of computing corrections to a detectors response owing to general detector motion, a straightforward way of connecting the results of numerical relativity simulations to gravitational wave detection, and a basis for a general and fully relativistic pulsar timing formula.

35 pages, 3 figures; submitted to Physical Review D

References in corpus (13)

• LIGO: The Laser Interferometer Gravitational-Wave Observatory
• TEMPO2, a new pulsar timing package. I: Overview
• Interferometer design of the KAGRA gravitational wave detector
• Tempo2, a new pulsar timing package. II: The timing model and precision estimates
• Testing General Relativity with Atom Interferometry
• A New Method for Gravitational Wave Detection with Atomic Sensors
• An Atomic Gravitational Wave Interferometric Sensor (AGIS)
• xPert: Computer algebra for metric perturbation theory
• General Relativistic Effects in Atom Interferometry
• High-frequency corrections to the detector response and their effect on searches for gravitational waves
• Space-borne gravitational wave detectors as time-delayed differential dynamometers
• Rightsizing LISA
• The North American Nanohertz Observatory for Gravitational Waves

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