The center-of-mass in Einsteins theory of gravitation

We prove the existence and uniqueness of a center-of-mass line as well as a center-of-motion line, the latter due toG. Dixon, 1964. The validity of the theorems depends on some assumptions listed in § 2, whose most restrictive ones (in the sense of physics) state a certain weakness of the gravitational field. In the concluding paragraph we give some corrolaries and a very simple application to the problem of motion.Essentially this work has been done during the authors stay at the Seminar f. Allg. Relativitätstheorie, Univ. Hamburg.