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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2022, Volume 62, Number 6, Pages 1016–1029
DOI: https://doi.org/10.31857/S0044466922060163
(Mi zvmmf11413)
 

This article is cited in 10 scientific papers (total in 10 papers)

Mathematical physics

Derivation of the equations of electrodynamics and gravity from the principle of least action

V. V. Vedenyapina, V. I. Parenkinab, S. R. Svirshchevskiia

a Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 125047, Moscow, Russia
b Moscow Region State University, 141014, Mytishchi, Moscow oblast, Russia
Citations (10)
Abstract: In classical works, field equations are given without deriving right-hand sides. In this paper, the right-hand sides of the Maxwell and Einstein equations are derived within the framework of Vlasov–Maxwell–Einstein equations from a classical, but more general least action principle.
Key words: Vlasov equation, Vlasov–Einstein equation, Vlasov–Maxwell equation, Vlasov–Poisson equation.
Received: 17.11.2021
Revised: 17.11.2021
Accepted: 24.12.2021
English version:
Computational Mathematics and Mathematical Physics, 2022, Volume 62, Issue 6, Pages 983–995
DOI: https://doi.org/10.1134/S096554252206015X
Bibliographic databases:
Document Type: Article
UDC: 517.958
Language: Russian
Citation: V. V. Vedenyapin, V. I. Parenkina, S. R. Svirshchevskii, “Derivation of the equations of electrodynamics and gravity from the principle of least action”, Zh. Vychisl. Mat. Mat. Fiz., 62:6 (2022), 1016–1029; Comput. Math. Math. Phys., 62:6 (2022), 983–995
Citation in format AMSBIB
\Bibitem{VedParSvi22}
\by V.~V.~Vedenyapin, V.~I.~Parenkina, S.~R.~Svirshchevskii
\paper Derivation of the equations of electrodynamics and gravity from the principle of least action
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2022
\vol 62
\issue 6
\pages 1016--1029
\mathnet{http://mi.mathnet.ru/zvmmf11413}
\crossref{https://doi.org/10.31857/S0044466922060163}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4452829}
\elib{https://elibrary.ru/item.asp?id=48506078}
\transl
\jour Comput. Math. Math. Phys.
\yr 2022
\vol 62
\issue 6
\pages 983--995
\crossref{https://doi.org/10.1134/S096554252206015X}
Linking options:
  • https://www.mathnet.ru/eng/zvmmf11413
  • https://www.mathnet.ru/eng/zvmmf/v62/i6/p1016
  • This publication is cited in the following 10 articles:
    1. V. V. Vedenyapin, N. N. Fimin, V. M. Chechetkin, “Vlasov–Maxwell–Einstein-type equations and their consequences. Applications to astrophysical problems”, Theoret. and Math. Phys., 218:2 (2024), 222–240  mathnet  crossref  crossref  mathscinet  adsnasa
    2. V. V. Vedenyapin, “On Derivation of Vlasov–Maxwell–Einstein Equations from the Principle of Least Action, the Hamilton–Jacobi Method, and the Milne–McCrea Model”, Dokl. Math., 2024  crossref
    3. V. V. Vedenyapin, A. A. Bay, “Least action principle for gravity and electrodynamics, the Lambda-term and the analog of Milne–McCrea solution for Lorentzian metric”, Eur. Phys. J. Plus, 139:2 (2024)  crossref
    4. Jiaping Sun, Chao Liang, Tiantang Yu, “Analytical assessment of dynamic stability in 2D unsaturated soil slopes reinforced with piles”, Arch. Civ. Mech. Eng., 25:1 (2024)  crossref
    5. V. V. Vedenyapin, “Mathematical Theory of the Expanding Universe Based on the Principle of Least Action”, Comput. Math. and Math. Phys., 64:11 (2024), 2624  crossref
    6. V. V. Vedenyapin, D. A. Kogtenev, “O vyvode i svoistvakh uravnenii tipa Vlasova”, Preprinty IPM im. M. V. Keldysha, 2023, 020, 18 pp.  mathnet  crossref
    7. V. V. Vedenyapin, N. N. Fimin, V. M. Chechetkin, “Hydrodynamic Consequences of Vlasov–Maxwell–Einstein Equations and Their Cosmological Applications”, Gravit. Cosmol., 29:1 (2023), 1  crossref
    8. Victor V. Vedenyapin, Nikolay N. Fimin, “Cosmological Aspects of the Theory of Equations of the Vlasov–Einstein Type and Their Consequences”, EQUATIONS, 3 (2023), 145  crossref
    9. V. V. Vedenyapin, A. A. Bay, A. G. Petrov, “On derivation of equations of gravitation from the principle of least action, relativistic Milne-Mccree solutions and Lagrange points”, Dokl. Math., 108:3 (2023), 481–485  mathnet  crossref  crossref  elib
    10. Victor V. Vedenyapin, Nikolay N. Fimin, Valery M. Chechetkin, “Cosmological aspects of hydrodynamic treatment of the Einstein–Vlasov equations”, Eur. Phys. J. Plus, 137:9 (2022)  crossref
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