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Description
The enhancement of the symmetry group for asymptotically flat spacetimes from the Poincare group to the infinite-dimensional BMS group gives a rich structure to the theory. The existence of supertranslations in the BMS group plays a key role in a variety of asymptotic phenomenon. In particular, there is a well-known "supertranslation ambiguity" in defining the angular momentum of an isolated gravitational system. Although this should be viewed as a generic feature of the theory, it does present the issue that, apriori, there may not seem to be a "preferred" definition of angular momentum. We propose a new criterion to assess the viability of definitions of angular momentum at null infinity: cross-section continuity. Although the Dray-Streubel (DS) definition automatically satisfies this condition due to the existence of a flux, the one-parameter family of angular momenta proposed by Compere and Nichols (CN) - which encompasses multiple other definitions - does not. We also verify the Chen-Wang-Yao (CWY) definition is cross-section continuous.