Zel'dovich and Polnarev, in their seminal paper on the displacement memory effect [1], suggested that particles hit by a burst of gravitational waves generated by flyby would be merely displaced. Their prediction is confirmed numerically for the wave profile which is the derivative of a Gaussian proposed by Gibbons and Hawking [2]. The study is extended to higher-order derivative profiles as proposed e.g. for gravitational collapse, etc.
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Zhang et al. (2024) studied this question.
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