Memory effect for impulsive gravitational waves

Impulsive gravitational plane waves, which have a δ-function singularity on a hypersurface, can be obtained by squeezing smooth plane gravitational waves with a Gaussian profile. They exhibit (as do their smooth counterparts) the velocity memory effect: after the wave has passed, particles initially at rest move apart with non-vanishing constant transverse velocity. A new effect is that, unlike the smooth case, (i) the velocities of particles originally at rest jump, (ii) the spacetime trajectories become discontinuous along the (lightlike) propagation direction of the wave.