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 
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/
@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},
     year = {1979},
     volume = {39},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1979_39_1_a7/}
}
TY  - JOUR
AU  - G. S. Asanov
TI  - Integrable covariant energy-momentum conservation law for the gravitational field with absolute parallelism structure
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1979
SP  - 75
EP  - 82
VL  - 39
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1979_39_1_a7/
LA  - ru
ID  - TMF_1979_39_1_a7
ER  - 
%0 Journal Article
%A G. S. Asanov
%T Integrable covariant energy-momentum conservation law for the gravitational field with absolute parallelism structure
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1979
%P 75-82
%V 39
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1979_39_1_a7/
%G ru
%F TMF_1979_39_1_a7

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] M. F. Shirokov, DAN SSSR, 195 (1970), 814 | Zbl

[2] M. F. Shirokov, Preprint ITP-72-13 IE, Kiev, 1972 | MR

[3] A. A. Logunov, V. N. Folomeshkin, TMF, 32 (1978), 147 | MR

[4] A. A. Logunov, V. N. Folomeshkin, TMF, 32 (1978), 167 | MR

[5] A. A. Logunov, V. N. Folomeshkin, TMF, 32 (1978), 291 | MR

[6] A. A. Logunov, V. N. Folomeshkin, TMF, 33 (1978), 174

[7] E. Cartan, Ann. Ec. Norm., 22 (1905), 268 | MR

[8] A. Einshtein, Sobranie nauchnykh trudov, t. II, «Nauka», 1966, str. 223

[9] G. Treder, Teoriya gravitatsii i printsip otnositelnosti, «Atomizdat», 1973

[10] V. I. Rodichev, Teoriya tyagoteniya v ortogonalnom repere, «Nauka», 1974 | MR

[11] G. S. Asanov, Ann. Physik, 34 (1977), 169 | DOI | MR

[12] G. S. Asanov, Rep. Math. Phys., 14 (1978), 239 | DOI | MR

[13] E. Cartan, Math. Ann., 102 (1930), 698 | DOI | MR | Zbl

[14] W. Slebodzinski, Exterior Forms and Their Applications, PWN, Warszawa, 1970 | MR | Zbl

[15] J. E. D'Atri, H. K. Nickerson, J. Differential Geometry, 2 (1968), 393 | DOI | MR | Zbl

[16] J. A. Wolf, J. Differential Geometry, 7 (1972), 19 | DOI | MR | Zbl