Displacement within velocity effect in gravitational wave memory

TL;DR

This paper investigates the conditions under which particles affected by gravitational waves exhibit pure displacement memory rather than velocity memory, supported by numerical and analytical examples.

Contribution

It identifies specific wave parameters that lead to pure displacement memory, expanding understanding of gravitational wave memory effects.

Findings

Particles can exhibit pure displacement memory at specific wave parameters.

Numerical simulations confirm the phenomenon with Gaussian profiles.

Analytical solutions are provided using Pöschl-Teller profiles.

Abstract

Particles initially at rest hit by a passing sandwich gravitational wave exhibit, in general, thevelocity memory effect (VM): they fly apart with constant velocity. For specific values of the wave parameters their motion can however become pure displacement (DM) as suggested by Zel'dovich and Polnarev. For such a ``miraculous'' value, the particle trajectory is composed of an integer number of (approximate) standing half-waves. Our statements are illustrated numerically by a Gaussian, and analytically by the P\"oschl-Teller profiles.