# Memory Effect and BMS-like Symmetries for Impulsive Gravitational Waves

## TL;DR

This paper investigates how impulsive gravitational waves influence test particles and geodesics, revealing measurable effects linked to BMS-like symmetries and memory effects that could be detected by future gravitational wave detectors.

## Contribution

It explicitly demonstrates the measurable impact of BMS-like symmetry parameters on geodesics caused by impulsive gravitational waves.

## Key findings

- BMS-like symmetries induce observable effects on test particles.
- Impulsive gravitational waves produce a memory effect on geodesics.
- Measurable geodesic deviations depend on BMS transformation parameters.

## Abstract

Cataclysmic astrophysical phenomena can produce impulsive gravitational waves that can possibly be detected by the advanced versions of present-day detectors in the future. Gluing of two spacetimes across a null surface produces impulsive gravitational waves (in the phraseology of Penrose [1]) having a Dirac Delta function type pulse profile along the surface. It is known that BMS-like symmetries appear as soldering freedom while we glue two spacetimes along a null surface. In this note, 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.