bsuirДоклады БГУИРDoklady BGUIR1729-76482708-0382БГУИР10.35596/1729-7648-2021-19-8-26-30bsuir-3240Research ArticleЭЛЕКТРОНИКА, РАДИОФИЗИКА, РАДИОТЕХНИКА, ИНФОРМАТИКАELECTRONICS, RADIOPHYSICS, RADIOENGINEERING, INFORMATICSGeometrization of the theory of electromagnetic and spinor fields on the background of the Schwarzschild spacetimeGeometrization of the theory of electromagnetic and spinor fields on the background of the Schwarzschild spacetimeKrylovaN. G.KrylovaN. G.

Nina Georgievna Krylova – PhD., Associate Professor, Associate Professor at Belarusian State Agrarian Technical University; Senior Researcher at Belarusian State University

220030, Republic of Belarus, Minsk, Nezavisimosti Ave., 4, Belarusian State University

nina-kr@tut.byRed’kovV. M.Red’kovV. M.

Victor M. Red’kov – D.Sc., Principal Researcher

Minsk

Belarusian State Agrarian Technical University; Belarusian State UniversityBelarusian State Agrarian Technical University; Belarusian State UniversityB.I. Stepanov Institute of Physics of the National Academy of Science of BelarusB.I. Stepanov Institute of Physics of the National Academy of Science of Belarus2021020120221982630Copyright © Krylova N.G., Red’kov V.M., 20222022Krylova N.G., Red’kov V.M.Krylova N.G., Red’kov V.M.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://doklady.bsuir.by/jour/article/view/3240

The geometrical Kosambi–Cartan–Chern approach has been applied to study the systems of differential equations which arise in quantum-mechanical problems of a particle on the background of non-Euclidean geometry. We calculate the geometrical invariants for the radial system of differential equations arising for electromagnetic and spinor fields on the background of the Schwarzschild spacetime. Because the second invariant is associated with the Jacobi field for geodesics deviation, we analyze its behavior in the vicinity of physically meaningful singular points r = M, ∞. We demonstrate that near the Schwarzschild horizon r = M the Jacobi instability exists and geodesics diverge for both considered problems.

The geometrical Kosambi–Cartan–Chern approach has been applied to study the systems of differential equations which arise in quantum-mechanical problems of a particle on the background of non-Euclidean geometry. We calculate the geometrical invariants for the radial system of differential equations arising for electromagnetic and spinor fields on the background of the Schwarzschild spacetime. Because the second invariant is associated with the Jacobi field for geodesics deviation, we analyze its behavior in the vicinity of physically meaningful singular points r = M, ∞. We demonstrate that near the Schwarzschild horizon r = M the Jacobi instability exists and geodesics diverge for both considered problems.

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The authors declare that there are no conflicts of interest present.