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The center-of-mass in Einsteins theory of gravitation

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Abstract

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.

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References

  1. Beiglböck, W.: Dissertation Universität Hamburg 1965. Report in International Conference on Relativistic Theories of Gravitation, vol. II, London 1965.

  2. Bondi, H.: Proc. Roy. Soc.A 282, 303 (1964).

    Google Scholar 

  3. Brehme, R. W., andB. S. de Witt: Ann. Phys.9, 220 (1960).

    Google Scholar 

  4. Dixon, G.: Nuovo Cimento X34, 317 (1964). Thesis Churchill University Cambridge 1965.

  5. Eddington, A.: Theory of relativity. Cambridge: University Press 1964.

    Google Scholar 

  6. Einstein, A.: Ann. Phys.49, 769 (1916).

    Google Scholar 

  7. ——, andB. Hoffmann: Ann. Math.39, 1, 65 (1938).

    Google Scholar 

  8. Eisenhart, L. P.: Riemannian geometry. Princeton: University Press 1949.

    Google Scholar 

  9. Fock, V.: J. Phys. U.S.S.R.1, 2 (1939).

    Google Scholar 

  10. Infeld, L., andJ. Plebanski: Motion and relativity. New York: Pergamon Press 1960.

    Google Scholar 

  11. Kobayashi, S., andK. Nomizu: Found. of Diff. Geometry I. New York: Interscience Publishers 1963.

    Google Scholar 

  12. Lanczos, C.: Z. Physik59, 514 (1929).

    Google Scholar 

  13. Møller, C.: Comm. Dublin Inst. Adv. StudiesA5 (1949).

  14. Papapetrou, A.: Ak. Athen14, 540 (1939); Proc. Roy. Soc.A 209, 248 (1951).

    Google Scholar 

  15. Pryce, C.: Proc. Roy. Soc.A 195 (1949).

  16. de Rham, G.: Variétés diff. Paris: Hermann 1955.

    Google Scholar 

  17. Schlesinger, L.: Math. Ann.99 (1928); Math. Z.33 (1931).

  18. Schouten, J. A.: Ricci calculus, 2nd ed. Berlin-Göttingen-Heidelberg: Springer 1954.

    Google Scholar 

  19. Synge, J.: Phys. Rev.47, 760 (1935); Relativity (SRT). Amsterdam: North Holland Publ. 1956.

    Google Scholar 

  20. Taub, A. H.: J. Math. Phys.5, 1, 112 (1964); Atti del Convegno Rel. Gen. Florence, Sept. 1964.

    Google Scholar 

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Authors and Affiliations

  1. Institut für Angewandte Mathematik der Universität Heidelberg, Germany

    W. Beiglböck

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  1. W. Beiglböck
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Additional information

Essentially this work has been done during the authors stay at the Seminar f. Allg. Relativitätstheorie, Univ. Hamburg.

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Beiglböck, W. The center-of-mass in Einsteins theory of gravitation. Commun.Math. Phys. 5, 106–130 (1967). https://doi.org/10.1007/BF01646841

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  • DOI: https://doi.org/10.1007/BF01646841

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