General Relativity and Gravitation

, Volume 9, Issue 10, pp 857–877 | Cite as

On a new variational principle in general relativity and the energy of the gravitational field

  • Jerzy Kijowski
Research Articles
Received:

Abstract

A new variational principle based on the affine connection in space-time is proposed. This leads to a new formulation of general relativity. The gravitational field is a field of inertial frames in space-time. The metricg appears as a momentum canonically conjugate to the gravitational field. In the case of simple matter fields, e.g., scalar fields, electromagnetic fields, Proca fields, or hydrodynamical matter, the new formulation is equivalent to the traditional one. A new formulation of conservation laws is proposed.

Keywords

General Relativity Electromagnetic Field Scalar Field Variational Principle Differential Geometry 
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.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Belinfante, F. J. (1940).Physica,7, 449.Google Scholar
  2. 2.
    Eddington, A. S. (1963).The Mathematical Theory of Relativity (University Press, Cambridge).Google Scholar
  3. 3.
    Einstein, A. (1915).Preuss. Akad. Wiss. Berlin, Sitzber., 884.Google Scholar
  4. 4.
    Einstein, A. (1925).Preuss. Akad. Wiss. Berlin, Sitzber., 414.Google Scholar
  5. 5.
    Hilbert, D. (1915).Königl. Gesel. Wiss. Göttingen, Nachr. Math.-Phys. Kl., 395.Google Scholar
  6. 6.
    Kijowski, J., and Tulczyjew, W. M., “A Symplectic Framework for Field Theories,” to appear inSpringer Lecture Notes in Physics.Google Scholar
  7. 7.
    Komar, A. (1959).Phys. Rev.,113, 934.Google Scholar
  8. 8.
    Misner, C. W., Thorne, K. S., and Wheeler, J. A. (1973).Gravitation (Freeman, San Francisco).Google Scholar
  9. 9.
    Møller, C. (1958).Ann. Phys. (N.Y.),4, 347.Google Scholar
  10. 10.
    Pirani, F. A. E. (1962). Gauss's theorem and gravitational energy, inLes Théories Relativistes de la Gravitation-Royaumont Conference 1959 (CNRS, Paris).Google Scholar
  11. 11.
    Rosenfeld, L. (1940).Acad. Roy. Belg.,18, 1.Google Scholar
  12. 12.
    Schrödinger, E. (1954).Space-Time Structure (University Press, Cambridge).Google Scholar
  13. 13.
    Szczyrba, W. (1976).Commun. Math. Phys.,51, 163.Google Scholar
  14. 14.
    Trautman, A. (1962). “Conservation Laws in General Relativity,” inGravitation-An Introduction to Current Research, ed. Witten, L. (Wiley, New York).Google Scholar
  15. 15.
    Tulczyjew, W. M. (1974).Symposia Math.,14, 247.Google Scholar

Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • Jerzy Kijowski
    • 1
  1. 1.Institute for Mathematical Methods in PhysicsUniversity of WarsawWarsawPoland

Personalised recommendations