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.
Highlights
The study of impulsive gravitational waves in the form of null shells was initiated by Penrose and others [1,2,3]
The long-studied BMS supertranslations at null infinity of asymptotically flat spaces are linked to the physics of soft gravitons [6,7,8], which appear to play an important role in restoring information not seen in the hard gravitons of Hawking radiation [9,10]
We have presented a new approach for studying congruences that cross a singular hypersurface
Summary
The study of impulsive gravitational waves in the form of null shells was initiated by Penrose and others [1,2,3]. The study of the effect of a null shell on a timelike congruence that crosses it has been addressed by Barrabes and Hogan [19,20] They calculated the change in the tangent vector and the geodesic deviation vector together with the expansion, shear, and rotation upon crossing an impulsive gravitational wave and found a jump in the acceleration of the geodesic and derivatives of the geodesic. We consider the simplest case of a null shell representing an outgoing gravitational wave and parametrized by a general soldering transformation (a subclass of which are the BMS supertranslations) in Minkowski space, but our method is applicable to any geodesic congruence that crosses a null shell localized on a Killing horizon. VI, we discuss our results and their relation to other formulations of gravitational memory—in particular, to that reviewed in Ref. [16]
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