The Brown-York mass of revolution surface in asymptotically Schwarzschild manifold

TL;DR

This paper proves that the Brown-York mass of convex revolution surfaces in an asymptotically Schwarzschild manifold converges to the ADM mass, establishing a link between quasi-local and global mass concepts in general relativity.

Contribution

It demonstrates the convergence of Brown-York mass to ADM mass for a specific class of surfaces in asymptotically Schwarzschild manifolds, providing new insights into mass definitions.

Findings

Brown-York mass converges to ADM mass for convex revolution surfaces

Establishes a connection between quasi-local and total mass in general relativity

Supports the validity of Brown-York mass as a measure of gravitational energy

Abstract

In this paper, we will show that the limit of the Brown-York mass of a family of convex revolution surfaces in an asymptotically Schwarzschild manifold is the ADM mass.