Geodesic
The energy-momentum problem and the theory of gravitation
Teoretičeskaâ i matematičeskaâ fizika, Tome 32 (1977) no. 3, pp. 291-325 Cet article a éte moissonné depuis la source Math-Net.Ru

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General properties of geometrised theories of gravitation are considered. Covariant formulation of conservation laws in arbitrary riemannian space-time is given. In the Einstein theory the symmetric as well as canonical energy-momentum tensor of the system “matter plus gravitational field” and, in particular, the energy-momentum of free gravitational waves, turns out to be equal to zero. To understand the origin of the problems and difficulties concerning the energy-momentum in the Einstein theory, the gravitational field is considered in the usual framevork of the Lorents-invariant field theory, just like any other physical field. Combination of the approach proposed with the Einstein's idea of geometrisation makes it possible to formulate the geometrised gravitation theory, in which there are no inner contradictions, the energy-momentum of gravitational field is defined precisely and all the knowr experimental facts [17] are described successfully. For strong gravitational fields, the predictions of the quasilinear geometrised theory under consideration are different from those of the gravitational theory in the Einstein formulation. Black holes are absent in the theory. Evaluation of the energy-flux of gravitational waves leads to unambiguous results and shows that the gravitational waves transfer the positive-definite energy. 
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A. A. Logunov; V. N. Folomeshkin. The energy-momentum problem and the theory of gravitation. Teoretičeskaâ i matematičeskaâ fizika, Tome 32 (1977) no. 3, pp. 291-325. http://geodesic.mathdoc.fr/item/TMF_1977_32_3_a0/

[1] N. I. Lobachevskii, Novye osnovaniya geometrii, Izd. Kazanskogo universiteta, Kazan, 1835

[2] B. Riemann, Nachr. Kön. Ges. Wiss. Göttingen, 13 (1863), 133

[3] A. Einstein, Sitz. preuss. Akad. Wiss., 2 (1914), 1030

[4] A. Einstein, Phys. Z., 15, 108 ; (1914), 176 | Zbl | Zbl

[5] A. Einstein, Ann. Phys., 49 (1916), 769 | DOI | Zbl

[6] A. Einstein, M. Grossman, Z. Math. Phys., 62 (1913), 225

[7] A. Einstein, Naturforsch. Ges. Zürich, 58 (1913), 284

[8] A. Einstein, Phys. Z., 14 (1913), 1249 | Zbl

[9] H. A. Lorentz, Versl. Kön. Akad. Wet. Amsterdam, 25 (1916), 1380 | MR | Zbl

[10] H. Bauer, Phys. Z., 19 (1918), 163 | Zbl

[11] E. Schrödinger, Phys. Z., 19 (1918), 4 | Zbl

[12] M. F. Shirokov, L. I. Budko, DAN SSSR, 172 (1967), 326

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

[14] L. I. Rudakova, DAN SSSR, 197 (1971), 1045

[15] V. N. Folomeshkin, Intern. J. Theor. Phys., 10 (1974), 145 ; 11 (1974), 387 ; Проблемы теории гравитации и элементарных частиц, No 6, Атомиздат, 1975, 91 | DOI | MR | DOI | MR

[16] A. A. Logunov, V. N. Folomeshkin, TMF, 32 (1977), 166 | Zbl

[17] A. A. Logunov, V. N. Folomeshkin, TMF, 32 (1977), 147 | MR | Zbl

[18] I. Newton, Philosophiae naturalis principia mathematica, London, 1686 | MR

[19] F. W. Bessel, Astr. Nachr., 10 (1833), 98 | DOI

[20] R. V. Eötvös, Math. und Natur. Ber. Ungarn., 8 (1890), 65; Beibl. Ann. Phys., 15 (1891), 688; Ann. Phys., 59 (1896), 354 | DOI | Zbl

[21] R. V. Eötvös, D. Pekar, E. Fekete, Ann. Phys., 68 (1922), 11 | DOI

[22] P. G. Roll, R. Krotkov, R. H. Dicke, Ann. Phys., 26 (1964), 442 | DOI | MR | Zbl

[23] V. B. Braginskii, V. I. Panov, ZhETF, 61 (1971), 875

[24] A. Einstein, Sitz. preuss. Akad. Wiss., 1 (1918), 154

[25] H. A. Lorentz, Versl. Kön. Akad. Wet. Amsterdam, 25 (1916), 468 | MR | Zbl

[26] T. Levi Civita, Rend. Acad. Lincei, 26 (1917), 381 | Zbl

[27] L. Rosenfeld, Mem. Acad. Roy. Belgique, 6 (1940), 30 | MR | Zbl

[28] F. J. Belinfante, Physica, 6 (1939), 887 ; 7 (1940), 449 | DOI | MR | Zbl | DOI | MR | Zbl

[29] V. A. Fok, Teoriya prostranstva, vremeni i tyagoteniya, Fizmatgiz, 1961

[30] H. A. Lorentz, Versl. Kön. Akad. Wet. Amsterdam, 23 (1915), 1073 | MR | Zbl

[31] D. Hilbert, Nachr. Kön. Ges Wiss. Göttingen, math.-phys. Kl., 3 (1915), 395

[32] A. Einstein, Sitz. preuss. Akad. Wiss., 2 (1916), 1111

[33] F. Klein, Nachr. Kön. Ges Wiss. Göttingen, math.-phys. Kl., 1917, 469 ; 1918, 171 ; 1918, 394 | Zbl | Zbl | Zbl

[34] H. Weyl, Ann. Phys., 54 (1917), 117 ; Raum, Zeit, Materie, Springer, Berlin, 1918 | DOI | Zbl | MR | Zbl

[35] E. P. Wigner, Rev. Mod. Phys, 29 (1957), 255 | DOI | MR | Zbl

[36] V. N. Folomeshkin, Preprint IHEP 71-120, Serpukhov, 1971 | MR | Zbl

[37] V. N. Folomeshkin, YaF, 6 (1967), 1080; Acta Phys. Polon., 36 (1969), 439 | Zbl

[38] C. Moller, Kgl. Dan. Vid. Selsk, Mat.-Fys. Medd., 31 (1959) | MR | Zbl

[39] A. S. Eddington, The Mathematical Theory of Relativity, University Press, Cambridge, 1923 | MR | Zbl

[40] P. Freud, Ann. Math., 40 (1939), 417 | DOI | MR | Zbl

[41] W. Pauli, Relativitätstheorie, Berlin, 1921 | Zbl

[42] R. Penrose, Relativity, Groups and Topology, eds. G. M. DeWitt, B. S. DeWitt, New-York, 1964, 565 | MR

[43] N. A. Chernikov, E. A. Tagirov, Ann. Inst. H. Poincare, 9 (1968), 109 | MR | Zbl

[44] C. G. Callan, S. Coleman, R. Jackiv, Ann. Phys., 59 (1970), 42 | DOI | MR | Zbl

[45] R. W. Brehme, B. S. DeWitt, Ann. Phys., 9 (1960), 220 | DOI | MR | Zbl

[46] J. M. Hobbs, Ann. Phys., 47 (1968), 141 | DOI

[47] V. A. Fok, “Problemy gravitatsii”, Tezisy dokladov vtoroi sovetskoi gravitatsionnoi konferentsii, Tbilisi, 1965, 3 | MR

[48] H. A. Lorentz, Versl. Kön. Akad. Wet. Amsterdam, 12 (1904), 986 | MR | Zbl

[49] H. Poincare, Rend circolo mat. Palermo, 21 (1906), 129 | DOI | Zbl

[50] A. Einstein, Ann. Phys., 17 (1905), 891 | DOI | Zbl

[51] H. Poincare, Bull. Sci. Math., 28 (1904), 302 | Zbl

[52] A. Einstein, L. Infeld, B. Hoffmann, Ann. Math., 39 (1938), 65 | DOI | MR | Zbl

[53] A. Einstein, L. Infeld, Ann. Math., 41 (1940), 455 ; Canad. J. Math., 1 (1949), 209 | DOI | MR | Zbl | DOI | MR | Zbl

[54] V. N. Folomeshkin, Preprint IHEP 72-92, Serpukhov, 1972