Geodesic
On momentum flow density of the gravitational field
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 17 (2021) no. 2, pp. 137-147 Cet article a éte moissonné depuis la source Math-Net.Ru

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Momentum is considered on the basis of the approach widely used in the calculus of variations and in the optimal control theory, where variation of a cost functional is investigated. In physical theory, it is the action functional. Action variation under Lie dragging can be expressed as a surface integral of some differential form. The momentum density flow is defined using this form. In this work, the momentum balance equation is obtained. This equation shows that the momentum field transforms into a momentum of a mass. Examples showing the momentum flow structure for a mass distribution representing a uniform thin layer are provided.
Keywords: action variation of the gravitational field, momentum flow density of the gravitational field, momentum balance equation, thin layer with uniform mass distribution. 
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O. I. Drivotin. On momentum flow density of the gravitational field. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 17 (2021) no. 2, pp. 137-147. http://geodesic.mathdoc.fr/item/VSPUI_2021_17_2_a3/

[1] Pontryagin L. S., Boltyanskiy V. G., Gamkrelidze R. V., Mischenko E. F., Mathematical theory of optimal processes, Nauka Publ, M., 1976, 392 pp. (In Russian) | MR

[2] Drivotin O. I., “On numerical solution of the optimal control problem based on a method using the second variation of a trajectory”, Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 15:2 (2019), 283–295 (In Russian) | DOI | MR

[3] Drivotin O. I., Mathematical foundations of the field theory, St. Petersburg University Press, St. Petersburg, 2010, 168 pp. (In Russian)

[4] Drivotin O. I., “Covariant formulation of the Vlasov equation”, Proceedings of International Particle Accelerators Conference, IPAC'2011, Kursaal, San Sebastian, 2011, 2277–2279

[5] Drivotin O. I., “Degenerate solutions of the Vlasov equation”, Proceedings of Russian Accelerator Conference, RuPAC'2012, St. Petersburg State University, St. Petersburg, 2012, 376–378

[6] Drivotin O. I., “Covariant description of phase space distributions”, Vestnik of Saint Petersburg University. Series 10. Applied Mathematics. Computer Science. Control Processes, 12:3 (2016), 39–52 (In Russian) | DOI | MR

[7] Abbot B. P., Abbot R., Abbot T. D. et al., “LIGO scientific collaboration and Virgo collaboration”, Physical Review Letters, 116:6 (2016), 061102 | DOI | MR

[8] Landau L. D., Lifshitz E. M., The field theory, Nauka Publ, M., 1973, 504 pp. (In Russian) | MR

[9] Carrol S., Spacetime and geometry. An introduction to general relativity, Addison Wesley, San Fransisco, 2004, 513 pp. | MR | Zbl

[10] Drivotin O. I., “Rigorous definition of the reference frame”, Vestnik of Saint Petersburg University. Series 10. Applied Mathematics. Computer Science. Control Processes, 2014, no. 4, 25–36