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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2015, Volume 19, Number 3, Pages 462–473 (Mi vsgtu1338)  

Differential Equations and Mathematical Physics

The complete solution of the Yang-Mills equations for centrally symmetric metric in the presence of electromagnetic field

L. N. Krivonosova, V. A. Luk'yanovb

a Nizhny Novgorod State Technical University, Nizhnii Novgorod, 603600, Russian Federation
b Zavolzhsk Branch of Nizhny Novgorod State Technical University, Zavolzhsk, Nizhegorodskaya obl., 606520, Russian Federation

Abstract: Previously, we found the complete solution of Yang–Mills equations for a centrally symmetric metric in 4-dimensional space of conformal torsion-free connection in the absence of the electromagnetic field. Later, in another article, we found a solution of the Yang–Mills equations for the same metric in the presence of an electromagnetic field of a special type, suggesting that its components depend not on the four, but only on two variables. There we compared the resulting solutions with the well-known Reissner–Nordstrom solution and indicated the reason why these solutions do not match. In this paper, we do not impose any prior restrictions on the components of the electromagnetic field. This greatly complicates the derivation of the Yang–Mills equations. However, all computational difficulties were overcome. It turned out that the solutions of these equations all the same depend only on two variables and new solutions, in addition to previously obtained, do not arise. Consequently, we have found all the solutions of the Yang-Mills equations for a centrally symmetric metric in the presence of an arbitrary electromagnetic field, agreed with the Yang–Mills equations in the torsion-free space (i.e., without sources). These solutions are expressed in terms of the Weierstrass elliptic function.

Keywords: curvature of the connection, Hodge operator, Einstein equations, Maxwell's equations, Yang–Mills equations, centrally symmetric metric, Weierstrass elliptic function, 4-manifold with conformal connection
Author to whom correspondence should be addressed

DOI: https://doi.org/10.14498/vsgtu1338

Full text: PDF file (688 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 514.822
MSC: 83E99, 83C22
Original article submitted 26/IX/2014
revision submitted – 02/III/2015

Citation: L. N. Krivonosov, V. A. Luk'yanov, “The complete solution of the Yang-Mills equations for centrally symmetric metric in the presence of electromagnetic field”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 19:3 (2015), 462–473

Citation in format AMSBIB
\Bibitem{KriLuk15}
\by L.~N.~Krivonosov, V.~A.~Luk'yanov
\paper The complete solution of the Yang-Mills equations for centrally symmetric metric
in the presence of electromagnetic field
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2015
\vol 19
\issue 3
\pages 462--473
\mathnet{http://mi.mathnet.ru/vsgtu1338}
\crossref{https://doi.org/10.14498/vsgtu1338}
\zmath{https://zbmath.org/?q=an:06968976}
\elib{https://elibrary.ru/item.asp?id=24554658}


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  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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