论文标题
角动量定义的横截面连续性
Cross-Section Continuity of Definitions of Angular Momentum
论文作者
论文摘要
我们介绍了“横截面连续性”的概念，作为无效的角动量定义的可行性，$ j $，在零无限范围内：如果一系列横截面，$ {\ nathcal c} _n $，null Innull Infinity的null Infinity of null Infinity of Cross $ {\ Mathcal c} $，然后是$ {\ Mathcal C} $，然后$ {\ MATHCAL C} _n $应在$ {\ Mathcal C} $上收敛到Angular Mommentum，$ J $。 Dray-Streubel（DS）的角动量定义自动满足了与此定义相关的明确通量的存在。但是，我们表明，COMPERE和NICHOLS（CN）提出的DS定义的单参数修改（包括许多其他替代定义）不能满足横截面的连续性。另一方面，我们证明了陈华（CWY）的定义确实满足了横截面的连续性标准。
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.
