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Abstract

The gravitational wave memory effect is a permanent change in the relative separations of a configuration of inertial test particles, initially at rest with respect to each other, which make up a gravitational wave detector, after a pulse of gravitational radiation passes. It is a phenomenon of both observational and theoretical interest, and there is a growing body of research on its various aspects.,Below we describe some of the questions regarding memory which we have raised and explored over the past five years, namely:,(I) Is it possible to provide a consistent and meaningful definition of the memory effect in spacetimes that are not asymptotically flat and thus lack a notion of null infinity (particularly, expanding cosmological spacetimes)?,(II) Why is the memory effect unique to four spacetime dimensions? ,(III) Can the nonlinear memory of Christodoulou be understood as a tidal effect as stress-energy passes a detector at null infinity? ,(IV) Does the ordinary memory of Bieri and Garfinkle "imitate" null memory for ultrarelativistic matter?,We answer these questions by explicitly calculating, within linearized gravity, the memory accompanying classical particle-scattering sources. We find that: ,(I) Memory can be defined using derivative-of-delta-function features in the Riemann curvature tensor radiating away from the scattering event, and we use this to study memory in a cosmological spacetime.,(II) These delta-derivative features appear only at sub-leading order in spacetimes of dimension greater than four and so are physically negligible. ,(III) Nonlinear memory is not a tidal effect, but a purely radiative phenomenon without Newtonian analog. ,(IV) Ordinary memory smoothly extrapolates to null memory, and null sources are not "double counted" in both ordinary and null memory.

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