Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia2421810.22363/2658-4670-2020-28-2-131-140Research ArticleSpinor field in a spherically symmetric Friedmann UniverseSahaBijan<p>Doctor of Physical and Mathematical Sciences, assistant professor of the Institute of Physical Research and Technologies of Peoples’ Friendship University of Russia (RUDN University), leading researcher at the Laboratory of Information Technologies of The Joint Institute for Nuclear Research</p>bijan64@mail.ruZakharovEvgeniy I.<p>student of the Institute of Physical Research and Technologies</p>zakharov.eugene1998@gmail.comRikhvitskyVictor S.<p>Master of physical and mathematical Sciences, Leading programmer of the Laboratory of Information Technologies</p>rqvtsk@mail.ruPeoples’ Friendship University of Russia (RUDN University)Joint Institute for Nuclear Research1512202028213114020072020Copyright © 2020, Saha В., Zakharov E.I., Rikhvitsky V.S.2020<p>In recent years spinor field is being used by many authors to address some burning issues of modern cosmology. The motive behind using the spinor field as a source for gravitational field lies on the fact that the spinor field not only can describe the different era of the evolution but also can simulate different substances such as perfect fluid and dark energy. Moreover, the spinor field is very sensitive to the gravitational one and depending on the gravitational field the spinor field can react differently and change the spacetime geometry and the spinor field itself differently. This paper provides a brief description of the nonlinear spinor field in the FriedmannLemaitre-Robertson-Walker (FLRW) model. The results are compared in Cartesian and spherical coordinates. It is shown that during the transition from Cartesian coordinates to spherical ones, the energy-momentum tensor acquires additional nonzero non-diagonal components that can impose restrictions on either spinor functions or metric ones.</p>spinor fieldFLRW modelCartesian coordinatesspherical coordinatesспинорное полемодель FLRWдекартовы координатысферические координаты[B. Saha and G. N. Shikin, “Interacting Spinor and Scalar Fields in Bianchi Type I Universe Filled with Perfect Fluid: Exact Self-consistent Solutions,” General Relativity and Gravitation, vol. 29, pp. 1099-1112, 1997. DOI: 10.1023/a:1018887024268.][B. Saha and G. N. Shikin, “Nonlinear Spinor Field in Bianchi type-I Universe filled with Perfect Fluid: Exact Self-consistent Solutions,” Journal of Mathematical Physics, vol. 38, pp. 5305-5318, 1997. DOI: 10.1063/1.531944.][B. Saha, “Spinor field in Bianchi type-I Universe: regular solutions,” Physical Review D, vol. 64, p. 123501, 2001. DOI: 10.1103/physrevd. 64.123501.][B. 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DOI: 10.1140/epjc/s10052-015-3698-9.][K. A. Bronnikov, Y. P. Rybakov, and B. Saha, “Spinor fields in spherical symmetry. Einstein-Dirac and other space-time,” European Physical Journal - Plus, vol. 135, p. 124, 2020. DOI: 10.1140/epjp/s13360-02000150-z.][B. Saha, “Spinor fields in spherically symmetric space-time,” European Physical Journal - Plus, vol. 133, p. 416, 2018. DOI: 10.1140/epjp/ i2018-12273-9.][B. Saha, “Spinor Field Nonlinearity and Space-Time Geometry,” Physics of Particles and Nuclei, vol. 49, no. 2, pp. 146-212, 2018. DOI: 10.1134/ S1063779618020065.]