Limit of quasilocal mass integrals in asymptotically hyperbolic manifolds

TL;DR

This paper demonstrates that in asymptotically hyperbolic manifolds, certain quasilocal mass integrals over coordinate spheres converge to the manifold's total mass, paralleling known results in asymptotically flat spaces.

Contribution

It establishes the limit of quasilocal mass integrals in AH manifolds as the total mass, extending the analogy with asymptotically flat cases.

Findings

Quasilocal mass integrals converge to the AH mass.

The result parallels the ADM mass limit in flat manifolds.

Provides a new understanding of mass in hyperbolic geometry.

Abstract

In this paper, we will show that the limit of some quasilocal mass integrals of the coordinate spheres in an asymptotically hyperbolic (AH) manifold is the mass integral of the AH manifold. This is the analogue of the well known result that the limit of the Brown-York mass of coordinate spheres is the ADM mass in an asymptotically flat manifold.