• Corpus ID: 117846533

# On the center of mass in general relativity

@article{Huang2011OnTC,
title={On the center of mass in general relativity},
author={Lan-Hsuan Huang},
journal={arXiv: Differential Geometry},
year={2011}
}
The classical notion of center of mass for an isolated system in general relativity is derived from the Hamiltonian formulation and represented by a flux integral at infinity. In contrast to mass and linear momentum which are well-defined for asymptotically flat manifolds, center of mass and angular momentum seem less well-understood, mainly because they appear as the lower order terms in the expansion of the data than those which determine mass and linear momentum. This article summarizes some…
51 Citations
• Mathematics
Classical and Quantum Gravity
• 2019
It is shown that the mass of an asymptotically flat manifold with a noncompact boundary can be computed in terms of limiting surface integrals involving the Einstein tensor of the interior metric and
• Mathematics
• 2022
Let (M, g) be an asymptotically flat Riemannian 3-manifold. We provide a short new proof based on Lyapunov-Schmidt reduction of the existence of an asymptotic foliation of (M, g) by constant mean
• Mathematics
International Mathematics Research Notices
• 2020
In this paper, we define an energy-momentum vector at the spatial infinity of either asymptotically flat or asymptotically hyperbolic initial data sets carrying a non-compact boundary. Under
In this paper we introduce a family of center of masses that complement the definition of the family of Gauss-Bonnet-Chern masses by Ge-Wang-Wu and Li-Nguyen. In order to prove the existence and the
• Physics
• 2017
We derive expressions for the total Hamiltonian energy of gravitating systems in higher dimensional theories in terms of the Riemann tensor, allowing a cosmological constant $\Lambda \in \mathbb{R}$.
Extreme mass-ratio inspirals, in which solar-mass compact bodies spiral into supermassive black holes, are an important potential source for gravitational wave detectors. Because of the extreme
• Mathematics
• 2015
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
• Mathematics
The Journal of Geometric Analysis
• 2016
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
• Physics
• 2010
We derive the equations of motion of an extended test body in the context of Einstein's theory of gravitation. The equations of motion are obtained via a multipolar approximation method and are given
• Mathematics
• 2011
We prove the spacetime positive mass theorem in dimensions less than eight. This theorem states that for any asymptotically flat initial data set satisfying the dominant energy condition, the ADM

## References

SHOWING 1-10 OF 27 REFERENCES

• Mathematics, Physics
• 2008
We discuss the center of mass of asymptotically flat manifolds. Our main result is that for a class of metrics that includes those which near infinity are conformally flat with vanishing scalar
• 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
• Physics
• 2011
We show that it is possible to perturb arbitrary vacuum asymptotically flat spacetimes to new ones having exactly the same energy and linear momentum, but with center of mass and angular momentum
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
An asymptotic symmetries theorem is proved under certain hypotheses on the behaviour of the metric at spatial infinity. This implies that the Einstein-von Freud-ADM mass can be invariantly assigned
We propose a definition of center of mass for asymptotically flat manifolds satisfying the Regge–Teitelboim condition at infinity. This definition has a coordinate-free expression and natural
• Physics, Mathematics
• 1981
We extend our previous proof of the positive mass conjecture to allow a more general asymptotic condition proposed by York. Hence we are able to prove that for an isolated physical system, the energy
• Mathematics
• 2005
In this note we study constant mean curvature surfaces in asymptotically flat 3-manifolds. We prove that, outside a given compact subset in an asymptotically flat 3-manifold with positive mass,