, Volume 37, Issue 3, pp 281–287 | Cite as

The bimetric theory of gravitation with a dynamic background metric

  • L. Sh. Grigoryan


We study the bimetric theory of gravitation with background metric γik. In contrast to the accepted point of view, in which γik, is a metric given a priori, we assume that γik is a dynamic variable determined from the condition that the total action of the gravitating system must be an extremum. As a result it turns out that (1) γik can be described by the Einstein equation in space-time with the metric γik and (2) the energy-momentum tensor of the graviational field γik, is the source of γik. In this sense γik can be considered a secondary field in relation to gik. We determine the conditions for existence of integral covariant conservation laws. Two of the latter have no analogs in the theory with the background metric given a priori.


Einstein Equation Total Action Dynamic Variable Dynamic Background Bimetric Theory 
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Literature cited

  1. 1.
    L. D. Landau and E. M. Lifshits,Field Theory [in Russian], Nauka, Moscow (1973).Google Scholar
  2. 2.
    L. Sh. Grigoryan,Astrofizika,30, 380 (1989).Google Scholar
  3. 3.
    N. Rosen,Phys. Rev.,57, 147 (1940).Google Scholar
  4. 4.
    A. Papapetrou,Proc. Roy. Irish Acad.,52A, 11 (1948).Google Scholar
  5. 5.
    N. Rosen,Ann. Phys.,22, 1 (1963).Google Scholar
  6. 6.
    N. Rosen, in:Third International School of Cosmology and Gravitation, Erice, 8–20 May, pp. 2–40.Google Scholar
  7. 7.
    L. P. Grishchuk, A. N. Petrov, and A. D. Popova,Commun. Math. Phys.,94, 379 (1984).Google Scholar
  8. 8.
    V. A. Fok,The Theory of Space, Time, and Gravitation [in Russian], Fizmatgiz, Moscow (1961).Google Scholar
  9. 9.
    A. A. Logunov,Lectures on the Theory of Relativity and Gravitation [in Russian], Nauka, Moscow (1987).Google Scholar
  10. 10.
    N. Rosen,Lett. Nuovo Cimento,25, 266 (1979).Google Scholar
  11. 11.
    N. Rosen,Found. Phys.,15, 997 (1985).Google Scholar
  12. 12.
    N. A. Chernikov, “The Equations of Gravitation in Hyperbolic Space” [in Russian], Preprint, OIYal, P2-92-192 (1992).Google Scholar
  13. 13.
    L. P. Eisenhart,Riemannian Geometry, Princeton University Press (1949).Google Scholar
  14. 14.
    A. P. Norden,Affine Connection Spaces [in Russian], Nauka, Moscow (1976).Google Scholar
  15. 15.
    N. A. Chernikov, “Hilebert's Variational Method and the Papapetrou Tensor” [in Russian], Preprint, OIYal, P2-87-683 (1987).Google Scholar
  16. 16.
    A. A. Saaryan and L. Sh. Grigoryan,Astrofizika,33, 107 (1990).Google Scholar
  17. 17.
    L. Sh. Grigorian and A. A. Saharian,Astrophys. Space Sci.,180, 39 (1991).Google Scholar
  18. 18.
    C. Brans and R. H. Dicke,Phys. Rev.,124, 925 (1961).Google Scholar
  19. 19.
    L. D. Landau and E. M. Lifshits,Quantum Mechanics [in Russian], Nauka, Moscow (1974).Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • L. Sh. Grigoryan
    • 1
    • 2
  1. 1.Institute for Applied Problems of PhysicsArmenian Academy of SciencesArmenia
  2. 2.Erevan State UniversityArmenia

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