Geodesic congruences, impulsive gravitational waves, and gravitational memory

Abstract

In this paper we introduce a new approach to the study of the effects that an impulsive wave, containing a mixture of material sources and gravitational waves, has on a geodesic congruence that traverses it. We find that the effect of the wave on the congruence is a discontinuity in the B-tensor of the congruence. Our results thus provide a detector independent and covariant characterization of gravitational memory. We note some similarities between our results and the study of soft gravitons and gravitational memory on I. * Electronic address: martino@fluiditj.com † Electronic address: demhov@bao.sci.am arXiv:1808.04886v3 [hep-th]

Memory effect and BMS-like symmetries for impulsive gravitational waves

“…We consider the case of the Schwarzschild black hole in Kruskal coordinate (2.15). For plane fronted waves a similar kind of memory effect has been reported in [30]. Here we extend that for spherical waves.…”

“…We denote N − to be the tangent to the congruence to the − side of Σ . Mathematically the effect of the congruence N + crossing the null-shell is obtained by applying a coordinate transformation between the coordinates x µ + to a common continuous coordinate x µ installed locally across the shell [30] 2 . This relation between coordinates are just what we call as soldering transformations and consequently, the quantities evaluated will carry the soldering parameters indicating memory effect.…”

“…The search of memory effect has also been extended to impulsive plane gravitational waves [28] 1 . Memory effect for plane-fronted impulsive waves on null geodesic congruence (massless test particles) has been found in [30], where BMS supertranslation type memory has been obtained. We extend these studies for timelike geodesics (test particles or detectors).…”

“…We discard the possibility of generating a non-vanishing twist to the congruence, initially possessing a zero-twist, after IGW pass through it. This is ensured from the evolution equation[30] of twist.…”

Geodesic congruences in exact plane wave spacetimes and the memory effect

“…We demonstrate shear-induced focusing which causes a permanent change in the expansion after the departure of the pulse. This is B-memory as introduced in [22]. In other words, it is the expansion, shear and rotation which may undergo a permanent change caused by the appearance of the pulse.…”