Displacement memory for flyby

TL;DR

This paper confirms that gravitational waves from flybys cause particle displacement, using numerical and analytical methods to analyze specific wave profiles and their effects.

Contribution

It provides a numerical and analytical validation of displacement memory effects caused by flyby gravitational waves, extending previous theoretical predictions.

Findings

Numerical confirmation of displacement memory effect.

Analytical approximation using P"oschl-Teller potential.

Discussion of higher-order derivative profiles.

Abstract

Zel'dovich and Polnarev, in their seminal paper [1] suggested that a gravitational wave generated by flyby would merely displace the particles. We confirm their prediction numerically by fine-tuning the wave profile proposed by Gibbons and Hawking [2], and then analytically for its approximation by a P\"oschl-Teller potential. Higher-order derivative profiles proposed for gravitational collapse, etc [2] are shortly discussed.