Observer dependence of angular momentum in general relativity and its relationship to the gravitational-wave memory effect

We define a procedure by which observers can measure a type ofspecial-relativistic linear and angular momentum $(P^a, J^{ab})$ at a point ina curved spacetime using only the spacetime geometry in a neighborhood of thatpoint. The method is chosen to yield the conventional results in stationaryspacetimes near future null infinity. We also explore the extent to which spatially separated observers can comparethe values of angular momentum that they measure and find consistent results.We define a generalization of parallel transport along curves which gives aprescription for transporting values of angular momentum along curves thatyields the correct result in special relativity. If observers use thisprescription, then they will find that the angular momenta they measure areobserver dependent, because of the effects of spacetime curvature. The observerdependence can be quantified by a kind of generalized holonomy. We show thatbursts of gravitational waves with memory generically give rise to a nontrivialgeneralized holonomy: there is, in this context, a close relation between theobserver dependence of angular momentum and the gravitational-wave memoryeffect.Comment: 19 pages, 2 figures. Matches version published in Phys. Rev. D with errors in Appendix A correcte