Flyby-induced displacement: analytic solution
Résumé
Approximating the derivative-of-the-Gaussian profile proposed by Gibbons and Hawking by the hyperbolic Scarf potential, the scattering of particles by a gravitational wave generated by flyby is described analytically by following the Nikiforov-Uvarov method applied to the Scarf potential. Pure displacement arises when the wave zone contains an integer number of half-waves. The results confirm the prediction of Zel'dovich and Polnarev.
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