• 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… 
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51 Citations
Highly Influential Citations
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Background Citations
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Methods Citations
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References

SHOWING 1-10 OF 27 REFERENCES

On the center of mass of isolated systems

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…

On the proof of the positive mass conjecture in general relativity

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…

Role of surface integrals in the Hamiltonian formulation of general relativity

Specifying Angular Momentum and Center of Mass for Vacuum Initial Data Sets

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…

The mass of an asymptotically flat manifold

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…

On the invariant mass conjecture in general relativity

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…

On the center of mass of isolated systems with general asymptotics

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…

The Poincaré group as the symmetry group of canonical general relativity

The energy and the linear momentum of space-times in general relativity

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…

On the uniqueness of the foliation of spheres of constant mean curvature in asymptotically flat 3-manifolds

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,…