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2022

Cross-Section Continuity of Definitions of Angular Momentum

Chen, Po-Ning, Paraizo, Daniel, Wald, Robert M. et al.

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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, ${\mathcal C}_n$, of null infinity converges uniformly to a cross-section ${\mathcal C}$, then the angular momentum, $J_n$, on ${\mathcal C}_n$ should converge to the angular momentum, $J$, on ${\mathcal C}$.

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 (CN) -- which encompasses numerous other alternative definitions -- does not satisfy cross-section continuity.
On the other hand, we prove that the Chen-Wang-Yau (CWY) definition does satisfy the cross-section continuity criterion.

Cross-Section Continuity of Definitions of Angular Momentum · Around

Built on

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P.T. Chrusciel, J. Jezierski, and J. Kijowski, Hamiltonian Field Theory in the Radiating Regime
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Then

G. Compere, A. Fiorucci, and R. Ruzziconi, JHEP 10
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2020
Later among the works it cites.
J. Keller, Y.-K. Wang, and S.-T. Yau, Adv. Theor. Math. Phys. 24
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P.-N. Chen, J. Keller, M.-T. Wang, Y.-K. Wang, and S.-T. Yau, Comm. Math. Phys. 386
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