The center of mass in general relativity

@article{Schattner1979TheCO,
  title={The center of mass in general relativity},
  author={Ruprecht Schattner},
  journal={General Relativity and Gravitation},
  year={1979},
  volume={10},
  pages={377-393}
}
In Dixon's theory of the dynamics of extended bodies in metric theories of gravity, a definition of a center-of-mass line is proposed. We prove the existence and uniqueness of a zero-linear-momentum vector field. Using this vector field we show the existence of a center-of-mass line which is a smooth timelike curve contained in a convex hull of the world-tube of the body. 

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