On the behavior of quasi-local mass at the infinity along nearly round surfaces

TL;DR

This paper investigates how quasi-local masses like Brown-York and Hawking behave at infinity on nearly round surfaces in asymptotically flat manifolds, linking their limits to the ADM mass.

Contribution

It introduces an intrinsic definition of nearly round surfaces and demonstrates their geometric invariants approximate the ADM mass at infinity.

Findings

Brown-York and Hawking masses converge to the ADM mass at infinity.

Nearly round surfaces can be used to approximate the total mass of the manifold.

Geometric invariants of these surfaces provide a new way to understand mass in general relativity.

Abstract

In this paper, we study the limiting behavior of the Brown-York mass and Hawking mass along nearly round surfaces at infinity of an asymptotically flat manifold. Nearly round surfaces can be defined in an intrinsic way. Our results show that the ADM mass of an asymptotically flat 3-manifold can be approximated by some geometric invariants of a family of nearly round surfaces which approach to infinity of the manifold.