Flyby-induced displacement: analytic solution

Abstract

The motion of particles hit by a burst of gravitational waves generated by flyby admits, for the derivative-of-the-Gaussian profile, only a numerical description. The profile can however be approximated by the hyperbolic Scarf potential which admits an exact analytic solution via the Nikiforov-Uvarov method. Our toy model is consistent with the prediction of Zel'dovich and Polnarev provided the wave amplitude takes certain ``magical'' values.

16 pages, 2 figures

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