Memory effect and BMS-like symmetries for impulsive gravitational waves

Cataclysmic astrophysical phenomena can produce impulsive gravitational waves that can possibly be detected by the advanced versions of present-day detectors in the future. The gluing of two spacetimes across a null surface produces impulsive gravitational waves (in the phraseology of Penrose) having a Dirac Delta function type pulse profile along the surface. It is known that Bondi-van der Burg-Matzner-Sachs (BMS)-like symmetries appear as soldering freedom while we glue two spacetimes along a null surface. In this paper, we study the effect of such impulsive gravitational waves on test particles (detectors) or geodesics. We show explicitly some measurable effects that depend on BMS-transformation parameters on timelike and null geodesics. BMS-like symmetry parameters carried by the gravitational wave leave some "memory" on test geodesics upon passing through them.