Quasi-local mass at the null infinity of the Vaidya spacetime

Abstract

There are two important statements regarding the Trautman-Bondi mass [1,8,5] at null infinity: one is the positivity [7,6], and the other is the Bondi mass loss formula [1], which are both global in nature. The positivity of the quasi-local mass can potentially lead to a local description at null infinity. This is confirmed for the Vaidya spacetime in this note. We study the Wang-Yau quasi-local mass on surfaces of fixed size at the null infinity of the Vaidya spacetime. The optimal embedding equation is solved explicitly and the quasi-local mass is evaluated in terms of the mass aspect function of the Vaidya spacetime.

15 pages

References in corpus (2)

• Quasilocal mass in general relativity
• Isometric embeddings into the Minkowski space and new quasi-local mass

Cited by in corpus (3)

• Quasi-Local Mass near the Singularity, the Event Horizon and the Null Infinity of Black Hole Spacetimes
• Quasi-local mass on unit spheres at spatial infinity
• The Isometric Embedding Problem in a Null Cone