Quasi-local mass on unit spheres at spatial infinity

Abstract

In this note, we compute the limit of the Wang-Yau quasi-local mass on unit spheres at spatial infinity of an asymptotically flat initial data set. Similar to the small sphere limit of the Wang-Yau quasi-local mass, we prove that the leading order term of the quasi-local mass recovers the stress-energy tensor. For a vacuum spacetime, the quasi-local mass decays faster and the leading order term is related to the Bel-Robinson tensor. Several new techniques of evaluating quasilocal mass are developed in this note.

24 pages

References in corpus (3)

• Isometric embeddings into the Minkowski space and new quasi-local mass
• The limiting behavior of the Liu-Yau quasi-local energy
• Quasi-local mass at the null infinity of the Vaidya spacetime