Advertisement

General Relativity and Gravitation

, Volume 27, Issue 6, pp 605–627 | Cite as

Remarks concerning the notion of free fall in axiomatic space-time theory

  • J. Schröter
  • U. Schelb
Article

Abstract

The notion of free fall plays a central role in EPS axiomatics. A constructive procedure for the detection of freely falling gravitational monopoles has been elaborated by Coleman and Korté. This was done in order to eliminate the vagueness of the primitive notion of free fall from spacetime theory. In this paper it is shown that neither the gravitational monopoles nor their free fall can be detected by the proposed procedure alone, without using physical laws beyond the mentioned spacetime theories. For this purpose, two examples of geodesic directing fields in a Schwarzschild space time are presented, one for particles obeying a special Lorentz-force equation and one for objects obeying Papapetrou's spinning particle equation. Two possibilities are discussed to overcome the difficulties of the constructive procedure.

Keywords

Differential Geometry Space Time Directing Field Free Fall Particle Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ehlers, J., Schild, A., Pirani, F. A. B. (1972). InGeneral Relativity, L. O. Raifeartaigh, ed. (Oxford University Press, Oxford).Google Scholar
  2. 2.
    Pirani, F. A. E. (1973). InSymposia Mathematica XII (Academic Press, London/New York).Google Scholar
  3. 3.
    Ehlers, J., Schild, A. (1973).Commun. Math. Phys. 32, 119.CrossRefGoogle Scholar
  4. 4.
    Reichenbach, H. (1979).Axiomatik der relativistischen Raum-Zeit-Lehre, Gesammelte Werke (Vieweg & Sohn, Braunschweig/Wiesbaden), vol. 3; English translation: (1969).Axiomatization of the Theory of Relativity (University of California Press, Berkeley and Los Angeles).Google Scholar
  5. 5.
    Woodhouse, N. M. J. (1973).J. Math. Phys. 14, 495.CrossRefGoogle Scholar
  6. 6.
    Perlick, V. (1980). “über die Ehlers-Pirani-Schild-Axiomatik der Allgemeinen RelativitÄtstheorie.” Preprint, Technical University Berlin; (1982/3). “Weyl-Mannigfaltigkeiten als Raum-Zeit-Modelle.” Diploma thesis, Technical University Berlin.Google Scholar
  7. 7.
    Meister, R. (1991). “Eine Neuformulierung der EPS-Axiomatik.” Diploma thesis, University of Paderborn.Google Scholar
  8. 8.
    Ludwig, G. (1990).Die Grundstrukturen einer physikalischen Theorie (2nd. ed., Springer-Verlag New York/Berlin/Heidelberg).Google Scholar
  9. 9.
    Coleman, R. A., Korté, H. (1980).J. Math. Phys. 21, 1340.CrossRefGoogle Scholar
  10. 10.
    Coleman, R. A., Korté, H. (1981).J. Math. Phys. 22, 2598.Google Scholar
  11. 11.
    Coleman, R. A., Korté, H. (1984).J. Math. Phys. 25, 3513.CrossRefGoogle Scholar
  12. 12.
    Ehlers, J., Köhler, E. (1977).J. Math. Phys. 18, 2014.CrossRefGoogle Scholar
  13. 13.
    Papapetrou, A. (1951).Proc. Roy. Soc. Lond. A209, 248.Google Scholar
  14. 14.
    Corinaldesi, E., Papapetrou, A. (1951).Proc. Roy. Soc. Lond. A209, 259.Google Scholar
  15. 15.
    Dixon, W. G. (1979). InProc. International School of Physics “Enrico Fermi,” LXVII, J. Ehlers, ed. (North-Holland, Amsterdam/New York).Google Scholar
  16. 16.
    Weyl, H. (1952).Space, Time and Matter (Dover, New York).Google Scholar
  17. 17.
    Heilig, U., Pfister, H. (1990).J. Geom. Phys. 7, 419.CrossRefGoogle Scholar
  18. 18.
    Coleman, A. R., Schmidt, H. J. (1993). “A Geometric Formulation of the Equivalence Principle”. Preprint, Zentrum für InterdisziplinÄre Forschung, UniversitÄt Bielefeld.Google Scholar
  19. 19.
    Brickell, F., Clark, R. S. (1970).Differential Manifolds. An Introduction (Van Nostrand, Rheinold, London).Google Scholar
  20. 20.
    Poor, W. (1981).Differential Geometric Structures (McGraw-Hill, New York).Google Scholar
  21. 21.
    Ambrose, W., Palais, R. S., Singer, I. M. (1960).Anais Academia Bras. de CiÊncias 32, 163.Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • J. Schröter
  • U. Schelb
    • 1
  1. 1.AG Theoretische PhysikUniversity of PaderbornPaderbornGermany

Personalised recommendations