We calculate the limits of the quasi-local angular momentum and center-of-mass defined by Chen–Wang–Yau [11] for a family of spacelike two-spheres approaching future null infinity in an asymptotically flat spacetime admitting a Bondi–Sachs expansion. Our result complements earlier work of Chen–Wang–Yau [12], where the authors calculate the limits of the quasi-local energy and linear momentum at null infinity. Finiteness of the center-of-mass limit requires that the spacetime be in the so-called center-of-mass frame, a mild assumption on the mass aspect function amounting to vanishing of linear momentum at null infinity. With this condition and the assumption that the Bondi mass is non-trivial, we obtain explicit expressions for the angular momentum and center-of-mass at future null infinity in terms of the observables appearing in the Bondi–Sachs expansion of the spacetime metric.

中文翻译：

---

评估零无穷大处的准局部角动量和质心

我们计算了由 Chen-Wang-Yau [11] 定义的准局域角动量和质心的极限，用于在一个渐近平坦的时空中接近未来零无穷大的类空间两个球体，允许 Bondi-Sachs 展开. 我们的结果补充了 Chen-Wang-Yau [12] 的早期工作，其中作者计算了零无穷大处的准局部能量和线性动量的极限。质心极限的有限性要求时空处于所谓的质心坐标系中，这是对质量纵横函数的温和假设，相当于在零无穷远处线性动量消失。有了这个条件和邦迪质量是非平凡的假设，