The authors derive exact analytic solutions for gravitational wave displacement memory when the flyby profile is approximated by the hyperbolic Scarf potential, with magic amplitude values |g|=(2n+1) sqrt(n(n+1)).
Gravitational wave memory: further examples
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abstract
Ehlers and Kundt [1] argued in favor of the velocity effect: particles initally at rest hit by a burst of gravitational waves should fly apart with constant velocity after the wave has passed. Zel'dovich and Polnarev [2] suggested instead that waves generated by flyby would be merely displaced. Their prediction is confirmed provided the wave parameters take some particular values.
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Flyby-induced displacement: analytic solution
The authors derive exact analytic solutions for gravitational wave displacement memory when the flyby profile is approximated by the hyperbolic Scarf potential, with magic amplitude values |g|=(2n+1) sqrt(n(n+1)).