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

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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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     author = {O. I. Drivotin},
     title = {On momentum flow density of the gravitational field},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {137--147},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2021_17_2_a3/}
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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/