Persistent gravitational wave observables: Nonlinear plane wave spacetimes

Abstract

In the first paper in this series, we introduced "persistent gravitational wave observables" as a framework for generalizing the gravitational wave memory effect. These observables are nonlocal in time and nonzero in the presence of gravitational radiation. We defined three specific examples of persistent observables: a generalization of geodesic deviation that allowed for arbitrary acceleration, a holonomy observable involving a closed curve, and an observable that can be measured using a spinning test particle. For linearized plane waves, we showed that our observables could be determined just from one, two, and three time integrals of the Riemann tensor along a central worldline, when the observers follow geodesics. In this paper, we compute these three persistent observables in nonlinear plane wave spacetimes, and we find that the fully nonlinear observables contain effects that differ qualitatively from the effects present in the observables at linear order. Many parts of these observables can be determined from two functions, the transverse Jacobi propagators, and their derivatives (for geodesic observers). These functions, at linear order in the spacetime curvature, reduce to the one, two, and three time integrals of the Riemann tensor mentioned above.

arXiv comment24 pages, 1 figure, 1 table; v2: fixed typos, matches published version

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Cited by in corpus (12)

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• Brans-Dicke theory in Bondi-Sachs form: Asymptotically flat solutions, asymptotic symmetries and gravitational-wave memory effects
• Persistent gravitational wave observables: Curve deviation in asymptotically flat spacetimes
• The First-Order Velocity Memory Effect from Compact Binary Coalescing Sources
• Celestial $w_{1+\infty }$ charges and the subleading structure of asymptotically-flat spacetimes
• A simple analytic example of the gravitational wave memory effect
• Persistent gravitational wave observables: Nonlinearities in (non-)geodesic deviation
• Gravitational wave memory and its effects on particles and fields
• Elliptically Polarized Plane Gravitational Waves
• Asymptotic Higher Spin Symmetries II: Noether Realization in Gravity
• Generalized geodesic deviation in de Sitter spacetime
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