Quasi-local mass integrals and the total mass

TL;DR

This paper demonstrates that specific quasi-local mass integrals, evaluated via the Ricci tensor on asymptotically flat and hyperbolic manifolds, converge to the total mass in all dimensions.

Contribution

It establishes the equivalence of Brown-York and Hawking quasi-local mass integrals to the total mass using Ricci tensor evaluations across all dimensions.

Findings

Quasi-local mass integrals converge to total mass

Results apply to all dimensions

Valid for asymptotically flat and hyperbolic manifolds

Abstract

On asymptotically flat and asymptotically hyperbolic manifolds, by evaluating the total mass via the Ricci tensor, we show that the limits of certain Brown-York type and Hawking type quasi-local mass integrals equal the total mass of the manifold in all dimensions.