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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Fock, V.A.: Theory of space, time, and gravitation. London: Pergamon 1959
Landau, L.D., Lifshitz, E.M.: The classical theory of fields. 3rd rev. English ed. Reading, MA. London: Addison-Wesley and Pergamon 1971
Misner, C.W., Thorne, K.S., Wheeler, J.A.: Gravitation. San Francisco: Freeman 1973
De Witt, B.S.: Dynamical theory of groups and fields. New York: Gordon and Breach 1965
Kraichnan, R.H.: Special-relativistic derivation of generally covariant gravitation theory. Phys. Rev.98, 1118–1122 (1955)
Weinberg, S.: Photons and gravitons in perturbation theory: derivations of Maxwell and Einstein equations. Phys. Rev. B138, 988–1002 (1965)
Ogiyevetsky, V.I., Polubarinov, I.V.: Interaction field of spin two and the Einstein equations. Ann. Phys.35, 167–208 (1965)
Deser, S.: Self-interaction and gauge invariance. G.R.G.1, 9–18 (1970)
Rosen, N.: Flat-space metric in general relativity theory. Ann. Phys.22, 1–10 (1963)
Thorne, K.S., Lee, D.L., Lightman, A.P.: Foundations for a theory of gravitation theories. Phys. Rev. D7, 3563–3578 (1973)
Deser, S., Laurent, B.E.: Gravitation without self-interaction. Ann. Phys.50, 76–101 (1968)
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 1982
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);
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)
Niedra, J.M., Janis, A.I.: Gravitational radiation in Robertson-Walker backgrounds. G.R.G.15, 241–254 (1983)
Isaacson, R.A.: Gravitational radiation in the limit of high frequency. Phys. Rev.166, 1263–1280 (1968)
Barnebey, T.A.: Gravitational waves: the nonlinearized theory. Phys. Rev. D10, 1741–1748 (1974)
Schouten, J.A.: Tensor analysis for physicists. Oxford: Clarendon Press 1951
Eisenhart, L.P.: Continuous groups of transformations. Princeton, NJ: Princeton University Press 1933
Teitelboim, C.: Quantum mechanics of the gravitational field. Phys. Rev. D25, 3159–3179 (1982)
Mitzkevich, N.V.: Physical fields in general relativity theory. Moscow: Nauka 1969 (in Russian)
Konopliova, N.P., Popov, V.N.: Gauge fields. Moscow: Atomizdat 1980 (in Russian)
Davis, W.R.: Classical fields, particles and the theory of relativity. New York: Gordon and Breach 1970
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)
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Communicated by Ya. G. Sinai
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Grishchuk, L.P., Petrov, A.N. & Popova, A.D. Exact theory of the (Einstein) gravitational field in an arbitrary background space-time. Commun.Math. Phys. 94, 379–396 (1984). https://doi.org/10.1007/BF01224832
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DOI: https://doi.org/10.1007/BF01224832