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# Advances in Theoretical and Mathematical Physics

## Volume 24 (2020)

### Number 6

### Evaluating quasi-local angular momentum and center-of-mass at null infinity

Pages: 1423 – 1473

DOI: https://dx.doi.org/10.4310/ATMP.2020.v24.n6.a3

#### Authors

#### Abstract

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.

S.-T. Yau was partially supported by NSF grant DMS-160781 and by Simons Foundation grant 385581.

Y.-K. Wang was supported by Taiwan MOTS grants 105-2115-M-006-016-MY2 and 107-2115-M-006-001-MY2.

Published 7 July 2021