## 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.

Original language | English |
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Pages (from-to) | 1423-1473 |

Number of pages | 51 |

Journal | Advances in Theoretical and Mathematical Physics |

Volume | 24 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2020 |

## All Science Journal Classification (ASJC) codes

- General Mathematics
- General Physics and Astronomy