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The symmetries of asymptotically flat spacetimes in general relativity aregiven by the Bondi-Metzner-Sachs (BMS) group, though there are proposedgeneralizations of its symmetry algebra. Associated with each symmetry is acharge and a flux, and the values of these charges and their changes cancharacterize a spacetime. The charges of the BMS group are relativistic angularmomentum and supermomentum (which includes 4-momentum); the extensions of theBMS algebra also include generalizations of angular momentum called "superangular momentum." Several different formalisms have been used to defineangular momentum, and they produce nonequivalent expressions for the charge. Itwas shown recently that these definitions can be summarized in a two-parameterfamily of angular momenta, which we investigate in this paper. We find thatrequiring that the angular momentum vanishes in flat spacetime restricts thetwo parameters to be equal. If we do not require that the angular momentumagrees with a common Hamiltonian definition, then we are left with aone-parameter family of angular momenta that includes the definitions from theseveral different formalisms. We then also propose a similar two-parameterfamily of super angular momentum. We examine the effect of the free parameterson the values of the angular momentum and super angular momentum fromnonprecessing binary-black-hole mergers. The definitions of angular momentumdiffer at a high post-Newtonian order for these systems, but only when thesystem is radiating gravitational waves. The different super-angular-momentumdefinitions occur at lower orders, and there is a difference in the change ofsuper angular momentum even after the gravitational waves pass, which arisesbecause of the gravitational-wave memory effect. We estimate the size of theseeffects using numerical-relativity surrogate waveforms and find they are smallbut resolvable.

Definitions of (super) angular momentum in asymptotically flat spacetimes: Properties and applications to compact-binary mergers