Geodesic
Integrable covariant energy-momentum conservation law for the gravitational field with absolute parallelism structure
Teoretičeskaâ i matematičeskaâ fizika, Tome 39 (1979) no. 1, pp. 75-82

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It is shown that the description of the gravitational field in a Riemannian space-time by means of an absolute parallelism structure makes it possible to formulate a covariant and integrable energy-momentum conservation law of the gravitational field by requiring vanishing of the covariant divergence of the energy-momentum tensor in the sense of absolute parallelism. As a result of allowance for the covariant constraints on the absolute parallelism tetrads, the Lagrangian density ceases to be geometrized and leads to a unique conservation law of such type in the $N$-body problem. From the covariant field equations there also follows the existence of special Euclidean coordinates outside static neighborhoods of gravitating bodies; in these coordinates, which are determined by the absolute parallelism tetrads, the linear approximation is not associated with noncovariant assumptions. 
@article{TMF_1979_39_1_a7,
     author = {G. S. Asanov},
     title = {Integrable covariant energy-momentum conservation law for the gravitational field with absolute parallelism structure},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {75--82},
     publisher = {mathdoc},
     volume = {39},
     number = {1},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1979_39_1_a7/}
}
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G. S. Asanov. Integrable covariant energy-momentum conservation law for the gravitational field with absolute parallelism structure. Teoretičeskaâ i matematičeskaâ fizika, Tome 39 (1979) no. 1, pp. 75-82. http://geodesic.mathdoc.fr/item/TMF_1979_39_1_a7/