Persistent gravitational wave observables: Nonlinearities in (non-)geodesic deviation

TL;DR

This paper explores nonlinear persistent gravitational wave observables, extending the understanding of memory effects beyond linear approximations, and introduces non-perturbative results applicable in various spacetime regions.

Contribution

It generalizes persistent gravitational wave observables, including displacement and drift memory, to non-perturbative regimes and non-asymptotically flat spacetimes, revealing deeper physical relationships.

Findings

Generalized displacement memory to include drift and ballistic memory.

Derived non-perturbative, higher-order effects on observer separation and proper time shifts.

Applicable to diverse spacetime geometries beyond linear approximations.

Abstract

The usual gravitational wave memory effect can be understood as a change in the separation of two initially comoving observers due to a burst of gravitational waves. Over the past few decades, a wide variety of other, "persistent" observables which measure permanent effects on idealized detectors have been introduced, each probing distinct physical effects. These observables can be defined in (regions of) any spacetime where there exists a notion of radiation, such as perturbation theory off of a fixed background, nonlinear plane wave spacetimes, or asymptotically flat spacetimes. Many of the persistent observables defined in the literature have only been considered in asymptotically flat spacetimes, and the perturbative nature of such calculations has occasionally obscured deeper relationships between these observables that hold more generally. The goal of this paper is to show how these more general results arise, and to do so we focus on two observables related to the separation between two, potentially accelerated observers. The first is the curve deviation, which is a natural generalization of the displacement memory, and also contains what this paper proposes to call drift memory (previously called "subleading displacement memory") and ballistic memory. The second is a relative proper time shift that arises between the two observers, either at second order in their initial separation and relative velocity, or in the presence of relative acceleration. The results of this paper are, where appropriate, entirely non-perturbative in the curvature of spacetime, and so could be used beyond leading order in asymptotically flat spacetimes.