Cross-section continuity of definitions of angular momentum. (19th January 2023)

• Record Type: Journal Article
• Authors: Chen, Po-Ning; Paraizo, Daniel E; Wald, Robert M; Wang, Mu-Tao; Wang, Ye-Kai; Yau, Shing-Tung
• Is Part Of: Classical and quantum gravity. Volume 40:Number 2(2023)
• Publication Date: 2023-01-19
• Subjects: general relativity -- angular momentum -- rotations; Quantum gravity -- Periodicals; Gravitation -- Periodicals; Relativity (Physics) -- Periodicals; Space and time -- Periodicals; Periodicals; 521.1
• DOI: 10.1088/1361-6382/acaa82
• Languages: English
• ISSNs: 0264-9381

Abstract

Abstract: 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.