A property of the Brown-York mass in Schwarzschild manifolds

TL;DR

This paper investigates the behavior of the Brown-York mass for a family of convex revolution surfaces in Schwarzschild manifolds, especially when these surfaces have unbounded ratios of their radii, extending previous results.

Contribution

It extends prior work by analyzing the limit of the Brown-York mass for more general convex revolution surfaces with unbounded radii ratios in Schwarzschild manifolds.

Findings

Established the limit behavior of Brown-York mass for these surfaces.

Extended previous results to a broader class of surfaces.

Provided new insights into geometric properties in Schwarzschild manifolds.

Abstract

We will extend partially our previous results about the limit of the Brown-York mass of a family of convex revolution surfaces in the Schwarzschild manifold such that these surfaces may have unbounded ratios of their radii.