Geometrization of the theory of electromagnetic and spinor fields on the background of the Schwarzschild spacetime
https://doi.org/10.35596/1729-7648-2021-19-8-26-30
Abstract
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.
About the Authors
N. G. Krylova
Belarusian State Agrarian Technical University;
Belarusian State University
Russian Federation
Russian Federation
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
V. M. Red’kov
B.I. Stepanov Institute of Physics of the National Academy of Science of Belarus
Russian Federation
Russian Federation
Victor M. Red’kov – D.Sc., Principal Researcher
Minsk
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Review
For citations:
Krylova N.G., Red’kov V.M. Geometrization of the theory of electromagnetic and spinor fields on the background of the Schwarzschild spacetime. Doklady BGUIR. 2021;19(8):26-30. https://doi.org/10.35596/1729-7648-2021-19-8-26-30
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