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

Jordan Keller (Black Hole Initiative, Harvard University, Cambridge, Massachusetts, U.S.A.)

Ye-Kai Wang (Department of Mathematics, National Cheng Kung University, Tainan City, Taiwan)

Shing-Tung Yau (Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)

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.

Published 7 July 2021