Integrable covariant energy-momentum conservation law for the gravitational field with absolute parallelism structure
G. S. Asanov
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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Theoretical and Mathematical Physics, 1979, 39:1, 331–335
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
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\paper Integrable covariant energy-momentum conservation law for the gravitational field with absolute parallelism structure
\jour Theoret. and Math. Phys.
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