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Displacement within velocity effect in gravitational wave memory
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Particles initially at rest hit by a passing sandwich gravitational wave exhibit, in general, thevelocity memory effect (VM): they fly apart with constant velocity. For specific values of the wave parameters their motion can however become pure displacement (DM) as suggested by Zel'dovich and Polnarev. For such a ``miraculous'' value, the particle trajectory is composed of an integer number of (approximate) standing half-waves. Our statements are illustrated numerically by a Gaussian, and analytically by the P\"oschl-Teller profiles.
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Memory Effect for deformed gravitational waves
Displacement memory in squeezed Pöschl–Teller gravitational waves is lost in the finite-amplitude impulsive limit; restoring it requires amplitudes that diverge as the squeezing parameter p→∞.
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