# The Brown–York Mass of Revolution Surfaces in Asymptotically Schwarzschild Manifolds

@article{Fan2009TheBM, title={The Brown–York Mass of Revolution Surfaces in Asymptotically Schwarzschild Manifolds}, author={Xu-Qian Fan and Kwok-Kun Kwong}, journal={Journal of Geometric Analysis}, year={2009}, volume={21}, pages={527-542} }

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.

## 8 Citations

A property of the Brown-York mass in Schwarzschild manifolds

- Physics, Mathematics
- 2012

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…

Limit of quasilocal mass integrals in asymptotically hyperbolic manifolds

- Mathematics
- 2010

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…

Quasi-local mass via isometric embeddings: a review from a geometric perspective

- Physics
- 2015

In this paper, we review geometric aspects of quasi-local energies proposed by Brown–York, Liu–Yau, and Wang–Yau. These quasi-local energy functions, having the important positivity property, share a…

On limit behavior of quasi-local mass for ellipsoids at spatial infinity

- Physics
- 2020

We discuss the spatial limit of the quasi-local mass for certain ellipsoids in an asymptotically flat static spherically symmetric spacetime. These ellipsoids are not nearly round but they are of…

On the Limiting Behaviors and Positivity of Quasi-local Mass

- Physics
- 2011

The concept of quasi-local masses was proposed by physicists about forty years ago to measure the energy of a given compact region by a closed spacelike 2-surface. There are several natural…

Hayward Quasilocal Energy of Tori

- Physics
- 2020

This paper is dedicated to the investigation of the positivity of the Hayward quasilocal energy of tori. Marginally trapped tori have nonnegative Hayward energy. We consider a scenario of a…

Quasi-Local Energy-Momentum and Angular Momentum in General Relativity

- Physics, MedicineLiving reviews in relativity
- 2009

The present status of the quasi-local mass, energy-momentum and angular-momentum constructions in general relativity is reviewed. First, the general ideas, concepts, and strategies, as well as the…

Mass of asymptotically flat $3$-manifolds with boundary

- Mathematics, Physics
- 2020

We study the mass of asymptotically flat $3$-manifolds with boundary using the method of Bray-Kazaras-Khuri-Stern. More precisely, we derive a mass formula on the union of an asymptotically flat…

## References

SHOWING 1-10 OF 23 REFERENCES

The mass of an asymptotically flat manifold

- Mathematics
- 1986

We show that the mass of an asymptotically flat n-manifold is a geometric invariant. The proof is based on harmonic coordinates and, to develop a suitable existence theory, results about elliptic…

Large-sphere and small-sphere limits of the Brown-York mass

- Mathematics, Physics
- 2007

In this paper, we will study the limiting behavior of the Brown-York mass of the coordinate spheres in an asymptotically flat manifold. Limiting behaviors of volumes of regions related to coordinate…

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

- Mathematics, Physics
- 2008

In this article, 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…

The inverse mean curvature flow and the Riemannian Penrose Inequality

- Mathematics
- 2001

Let M be an asymptotically flat 3-manifold of nonnegative scalar curvature. The Riemannian Penrose Inequality states that the area of an outermost minimal surface N in M is bounded by the ADM mass m…

Differential geometry of curves and surfaces

- Mathematics, Computer Science
- 1976

This paper presents a meta-geometry of Surfaces: Isometrics Conformal Maps, which describes how the model derived from the Gauss Map changed over time to reflect the role of curvature in the model construction.

On the proof of the positive mass conjecture in general relativity

- Mathematics
- 1979

LetM be a space-time whose local mass density is non-negative everywhere. Then we prove that the total mass ofM as viewed from spatial infinity (the ADM mass) must be positive unlessM is the flat…

Positive Mass Theorem and the Boundary Behaviors of Compact Manifolds with Nonnegative Scalar Curvature

- Mathematics, Physics
- 2002

In this paper, we study the boundary behaviors of compact manifolds with nonnegative scalar curvature and with nonempty boundary. Using a general version of Positive Mass Theorem of Schoen-Yau and…

Center of mass integral in canonical general relativity

- Physics
- 2003

Abstract For a two-surface B tending to an infinite-radius round sphere at spatial infinity, we consider the Brown–York boundary integral HB belonging to the energy sector of the gravitational…

On Geometric Problems Related to Brown-York and Liu-Yau Quasilocal Mass

- Physics, Mathematics
- 2010

We discuss some geometric problems related to the definitions of quasilocal mass proposed by Brown and York (Contemporary mathematics, vol 132, American Mathematical Society, Providence, pp 129–142,…

The Gravitational Hamiltonian, action, entropy and surface terms

- Physics
- 1996

We give a derivation of the gravitational Hamiltonian starting from the Einstein - Hilbert action, keeping track of all surface terms. This derivation can be applied to any spacetime that…