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 TMF, 1979, Volume 39, Number 1, Pages 75–82 (Mi tmf2601)

Integrable covariant energy-momentum conservation law for the gravitational field with absolute parallelism structure

G. S. Asanov

Abstract: 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.

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English version:
Theoretical and Mathematical Physics, 1979, 39:1, 331–335

Citation: G. S. Asanov, “Integrable covariant energy-momentum conservation law for the gravitational field with absolute parallelism structure”, TMF, 39:1 (1979), 75–82; Theoret. and Math. Phys., 39:1 (1979), 331–335

Citation in format AMSBIB
\Bibitem{Asa79} \by G.~S.~Asanov \paper Integrable covariant energy-momentum conservation law for the gravitational field with absolute parallelism structure \jour TMF \yr 1979 \vol 39 \issue 1 \pages 75--82 \mathnet{http://mi.mathnet.ru/tmf2601} \transl \jour Theoret. and Math. Phys. \yr 1979 \vol 39 \issue 1 \pages 331--335 \crossref{https://doi.org/10.1007/BF01018945}