Persistent gravitational wave observables: Nonlinear plane wave spacetimes

TL;DR

This paper extends the concept of persistent gravitational wave observables to nonlinear plane wave spacetimes, revealing new effects and showing how these observables relate to transverse Jacobi propagators, thus generalizing previous linear results.

Contribution

It computes nonlinear plane wave observables, demonstrating qualitative differences from linear cases and linking them to transverse Jacobi propagators.

Findings

Nonlinear observables contain effects absent at linear order.

Many observables can be derived from transverse Jacobi propagators.

Linear order observables reduce to integrals of the Riemann tensor.

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.