Communications in Mathematical Physics

, Volume 94, Issue 3, pp 379–396 | Cite as

Exact theory of the (Einstein) gravitational field in an arbitrary background space-time

  • L. P. Grishchuk
  • A. N. Petrov
  • A. D. Popova
Article

Abstract

The Lagrangian based theory of the gravitational field and its sources at the arbitrary background space-time is developed. The equations of motion and the energy-momentum tensor of the gravitational field are derived by applying the variational principle. The gauge symmetries of the theory and the associated conservation laws are investigated. Some properties of the energymomentum tensor of the gravitational field are described in detail and the examples of its application are given. The desire to have the total energymomentum tensor as a source for the linear part of the gravitational field leads to the universal coupling of gravity with other fields (as well as to the self-interaction) and finally to the Einstein theory.

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References

  1. 1.
    Fock, V.A.: Theory of space, time, and gravitation. London: Pergamon 1959Google Scholar
  2. 2.
    Landau, L.D., Lifshitz, E.M.: The classical theory of fields. 3rd rev. English ed. Reading, MA. London: Addison-Wesley and Pergamon 1971Google Scholar
  3. 3.
    Misner, C.W., Thorne, K.S., Wheeler, J.A.: Gravitation. San Francisco: Freeman 1973Google Scholar
  4. 4.
    De Witt, B.S.: Dynamical theory of groups and fields. New York: Gordon and Breach 1965Google Scholar
  5. 5.
    Kraichnan, R.H.: Special-relativistic derivation of generally covariant gravitation theory. Phys. Rev.98, 1118–1122 (1955)Google Scholar
  6. 6.
    Weinberg, S.: Photons and gravitons in perturbation theory: derivations of Maxwell and Einstein equations. Phys. Rev. B138, 988–1002 (1965)Google Scholar
  7. 7.
    Ogiyevetsky, V.I., Polubarinov, I.V.: Interaction field of spin two and the Einstein equations. Ann. Phys.35, 167–208 (1965)Google Scholar
  8. 8.
    Deser, S.: Self-interaction and gauge invariance. G.R.G.1, 9–18 (1970)Google Scholar
  9. 9.
    Rosen, N.: Flat-space metric in general relativity theory. Ann. Phys.22, 1–10 (1963)Google Scholar
  10. 10.
    Thorne, K.S., Lee, D.L., Lightman, A.P.: Foundations for a theory of gravitation theories. Phys. Rev. D7, 3563–3578 (1973)Google Scholar
  11. 11.
    Deser, S., Laurent, B.E.: Gravitation without self-interaction. Ann. Phys.50, 76–101 (1968)Google Scholar
  12. 12.
    Grishchuk, L.P., Zeldovich, Ya.B.: Complete cosmological theories. In: Quantum structure of space and time. Duff. M.J., Isham, C.J. (eds.). Cambridge: Cambridge University Press 1982Google Scholar
  13. 13.a)
    Grishchuk, L.P., Popova, A.D.: Gauge conditions for fields of higher spins in an external gravitational field. Sov. Phys. J.E.T.P.53, 1–8 (1981);Google Scholar
  14. 13.b)
    Grishchuk, L.P., Popova, A.D. Space-times admitting the complete set of the gauge conditions for higher spin fields. J. Phys. A: Math. Gen.15, 3525–3530 (1982)Google Scholar
  15. 14.
    Niedra, J.M., Janis, A.I.: Gravitational radiation in Robertson-Walker backgrounds. G.R.G.15, 241–254 (1983)Google Scholar
  16. 15. a)
    Isaacson, R.A.: Gravitational radiation in the limit of high frequency. Phys. Rev.166, 1263–1280 (1968)Google Scholar
  17. 15. b)
    Barnebey, T.A.: Gravitational waves: the nonlinearized theory. Phys. Rev. D10, 1741–1748 (1974)Google Scholar
  18. 16. a)
    Schouten, J.A.: Tensor analysis for physicists. Oxford: Clarendon Press 1951Google Scholar
  19. 16. b)
    Eisenhart, L.P.: Continuous groups of transformations. Princeton, NJ: Princeton University Press 1933Google Scholar
  20. 17.
    Teitelboim, C.: Quantum mechanics of the gravitational field. Phys. Rev. D25, 3159–3179 (1982)Google Scholar
  21. 18. a)
    Mitzkevich, N.V.: Physical fields in general relativity theory. Moscow: Nauka 1969 (in Russian)Google Scholar
  22. 18. b)
    Konopliova, N.P., Popov, V.N.: Gauge fields. Moscow: Atomizdat 1980 (in Russian)Google Scholar
  23. 19.
    Davis, W.R.: Classical fields, particles and the theory of relativity. New York: Gordon and Breach 1970Google Scholar
  24. 20.
    Grishchuk, L.P., Kopeykin, S.M.: On the motion of gravitating bodies with the radiation reaction force taken into account. Sov. Astron.: Pisma Astronom. J.9, 436–440 (1983)Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • L. P. Grishchuk
    • 1
  • A. N. Petrov
    • 1
  • A. D. Popova
    • 2
  1. 1.Sternberg Astronomical InstituteMoscowUSSR
  2. 2.Institute of Scientific InformationMoscowUSSR

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