The memory effect for plane gravitational waves

P.-M Zhang,C Duval,G.W Gibbons,P.A Horvathy

doi:10.1016/j.physletb.2017.07.050

Abstract

We give an account of the gravitational memory effect in the presence of the exact plane wave solution of Einstein's vacuum equations. This allows an elementary but exact description of the soft gravitons and how their presence may be detected by observing the motion of freely falling particles. The theorem of Bondi and Pirani on caustics (for which we present a new proof) implies that the asymptotic relative velocity is constant but not zero, in contradiction with the permanent displacement claimed by Zel'dovich and Polnarev. A non-vanishing asymptotic relative velocity might be used to detect gravitational waves through the “velocity memory effect”, considered by Braginsky, Thorne, Grishchuk, and Polnarev.

Highlights

The theorem of Bondi and Pirani on caustics implies that the asymptotic relative velocity is constant but not zero, in contradiction with the permanent displacement claimed by Zel’dovich and Polnarev
By “gravitational memory effect” is meant that a system of freely falling particles initially at relative rest are displaced after the passing of a burst of gravitational radiation [1, 2]
The original proposal of Zel’dovich and Polnarev [1] claimed that detectors originally at rest will be displaced and will have vanishingly small relative velocity, in contrast with later findings of Bondi and Pirani [7]

Summary

INTRODUCTION

By “gravitational memory effect” is meant that a system of freely falling particles (viewed as detectors) initially at relative rest are displaced after the passing of a burst of gravitational radiation [1, 2]. The original proposal of Zel’dovich and Polnarev [1] claimed that detectors originally at rest will be displaced and will have vanishingly small relative velocity, in contrast with later findings of Bondi and Pirani [7]. A “velocity memory effect” highlighted by nonvanishing asymptotic relative velocity was considered by Braginsky, Grishchuk, Thorne, and Polnarev [2, 8, 9] and more recently, by Lasenby [4]. Our results might have some relevance for detecting gravitational waves through the “velocity memory effect” [2, 4, 8, 9, 16]

PLANE GRAVITATIONAL WAVES

ILLUSTRATION BY TISSOT DIAGRAM

SOFT GRAVITONS

CONCLUSION