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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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