Kavli Affiliate: Robert M. Wald
| First 5 Authors: Po-Ning Chen, Daniel Paraizo, Robert M. Wald, Mu-Tao Wang, Ye-Kai Wang
| Summary:
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.
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