Memory Effect of Gravitational Wave Pulses in PP-Wave Spacetimes

TL;DR

This paper investigates the gravitational memory effect caused by ramp-profile gravitational wave pulses in pp-wave spacetimes, analyzing geodesic evolution and confirming the universality of the memory effect across different pulse profiles.

Contribution

It provides analytical solutions for geodesic equations in pp-wave spacetimes with ramp pulses and demonstrates the universal nature of gravitational wave memory effects.

Findings

Separation between geodesics increases monotonically after pulse

Relative velocity between geodesics settles to a non-zero constant

Memory effect persists after the pulse dissipates

Abstract

In this paper, we study the gravitational memory effect in pp-wave spacetimes due to the passage of a pulse having the form of a ramp profile through this spacetime. We have analyzed the effect of this pulse on the evolution of nearby geodesics, and have determined analytical solutions of the geodesic equations in the Brinkmann coordinates. We have also examined the changes in the separation between a pair of geodesics and their velocity profiles. The separation (along $ x $ or $ y $-direction) increases monotonically from an initial constant value. In contrast, the relative velocity grows from zero and settles to a final non-zero constant value. These resulting changes are retained as memory after the pulse dies out. The nature of this memory is similar to that determined by earlier workers using Gaussian, square, and other pulse profiles, thereby validating the universality of gravitational wave memory.