On limit behavior of quasi-local mass for ellipsoids at spatial infinity**X He is partially supported by the Natural Science Foundation of Hunan Province (Grant 2018JJ2073). N Xie is partially supported by the National Natural Science Foundation of China (Grant 11671089).

Abstract

We discuss the spatial limit of the quasi-local mass for certain ellipsoids in an asymptotically flat static spherically symmetric spacetime. These ellipsoids are not nearly round but they are of interest as an admissible parametrized foliation defining the Arnowitt–Deser–Misner mass. The Hawking mass of this family of ellipsoids tends to . In contrast, we show that the Hayward mass converges to a finite value. Moreover, a positive mass type theorem is established. The limit of the mass has a uniform positive lower bound no matter how oblate these ellipsoids are. This result could be extended for asymptotically Schwarzschild manifolds. And numerical simulation in the Schwarzschild spacetime illustrates that the Hayward mass is monotonically increasing near infinity.