Quasi-local mass at null infinity in bondi-sachs coordinates

There are two chief statements regarding the Bondi-Trautman mass [3, 29, 37, 33, 34] at null infinity: one is the positivity [30, 20], and the other is the mass loss formula [3], which are both global in nature. In this note, we compute the limit of the Wang-Yau quasi-local mass on unit spheres at null infinity of an asymptotically flat spacetime in the Bondi-Sachs coordinates. The quasi-local mass leads to a local description of radiation that is purely gravitational at null infinity. In particular, the quasi-local mass is evaluated in terms of the news function of the Bondi-Sachs coordinates.