Cross-section continuity of definitions of angular momentum

Po Ning Chen, Daniel E. Paraizo, Robert M. Wald*, Mu Tao Wang, Ye Kai Wang, Shing Tung Yau

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We introduce a notion of ‘cross-section continuity’ as a criterion for the viability of definitions of angular momentum, J, at null infinity: If a sequence of cross-sections, , of null infinity converges uniformly to a cross-section , then the angular momentum, J n , on should converge to the angular momentum, J, on . The Dray-Streubel (DS) definition of angular momentum automatically satisfies this criterion by virtue of the existence of a well defined flux associated with this definition. However, we show that the one-parameter modification of the DS definition proposed by Compere and Nichols—which encompasses numerous other alternative definitions—does not satisfy cross-section continuity. On the other hand, we prove that the Chen-Wang-Yau definition does satisfy the cross-section continuity criterion.

Original languageEnglish
Article number025007
JournalClassical and Quantum Gravity
Issue number2
StatePublished - 19 Jan 2023


  • angular momentum
  • general relativity
  • rotations


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