Research Articles

General Relativity and Gravitation

, Volume 10, Issue 5, pp 377-393

First online:

The center of mass in general relativity

  • R. SchattnerAffiliated withMax-Planck-Institut für Physik und Astrophysik

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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.