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 TMF, 1977, Volume 32, Number 2, Pages 147–166 (Mi tmf3146)

Geometrized theories of gravitation

A. A. Logunov, V. N. Folomeshkin

Abstract: General properties of geometrized theories of gravitation are considered. Geometrization of the theory is performed only to the extent which is necessarily prescribed by the experiment (the geometrization of the Lagrangian density of matter only). Im the general case, equations of gravitational field and equations of motion of the matter are formulated in different riemannian spaces. Covariant formulation of the energymomentum conservation laws in arbitrary geometrized theory is given. In this formulation of conservation laws, introduction of the noncovariant notion of “pseudotensor” is not required. In completely geometrized theory (e.g., in the Einstein theory) free gravitational waves do not transfer any energy. But if, by the analogy with other physical fields, we require the gravitational waves to transfer energy and momentum, the Lagrangian of the gravitational field should not be geometrized. Properties of one of the variants of quasilinear geometrized theory describing experimental facts are considered. In this theory the fundamental static solution with spherical symmetry possesses the singularity only in the centre of coordinates and as a consequence, thereare no black holes in the theory. The theory makes it possible to formulate a satisfying model of homogeneous nonstationary Universe.

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English version:
Theoretical and Mathematical Physics, 1977, 32:2, 653–666

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Citation: A. A. Logunov, V. N. Folomeshkin, “Geometrized theories of gravitation”, TMF, 32:2 (1977), 147–166; Theoret. and Math. Phys., 32:2 (1977), 653–666

Citation in format AMSBIB
\Bibitem{LogFol77} \by A.~A.~Logunov, V.~N.~Folomeshkin \paper Geometrized theories of gravitation \jour TMF \yr 1977 \vol 32 \issue 2 \pages 147--166 \mathnet{http://mi.mathnet.ru/tmf3146} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=469110} \zmath{https://zbmath.org/?q=an:0385.53011} \transl \jour Theoret. and Math. Phys. \yr 1977 \vol 32 \issue 2 \pages 653--666 \crossref{https://doi.org/10.1007/BF01036328} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. A. Logunov, V. N. Folomeshkin, “Energy-momentum of gravitational waves in the general theory of relativity”, Theoret. and Math. Phys., 32:2 (1977), 667–672
2. A. A. Logunov, V. N. Folomeshkin, “The energy-momentum problem and the theory of gravitation”, Theoret. and Math. Phys., 32:3 (1977), 749–771
3. A. A. Logunov, V. N. Folomeshkin, “Does the energy of the source change when gravitational waves are emitted in Einstein's theory of gravitation?”, Theoret. and Math. Phys., 33:2 (1977), 952–959
4. G. S. Asanov, “Integrable covariant energy-momentum conservation law for the gravitational field with absolute parallelism structure”, Theoret. and Math. Phys., 39:1 (1979), 331–335
5. A. A. Logunov, V. I. Denisov, A. A. Vlasov, M. A. Mestvirishvili, V. N. Folomeshkin, “New concepts of space-time and gravitation”, Theoret. and Math. Phys., 40:3 (1979), 753–777
6. V. I. Denisov, A. A. Logunov, “New theory of space-time and gravitation”, Theoret. and Math. Phys., 50:1 (1982), 1–48
7. V. I. Denisov, V. O. Soloviev, “The energy determined in general relativity on the basis of the traditional Hamiltonian approach does not have physical meaning”, Theoret. and Math. Phys., 56:2 (1983), 832–841
8. V. I. Denisov, “Development of the concept of natural geometry for physical interactions”, Theoret. and Math. Phys., 191:2 (2017), 649–654
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