Flyby-induced displacement: analytic solution
arXiv:2502.01326 · doi:10.1016/j.physletb.2025.139687
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