Soliton-Like Spherical Symmetric Solutions of the Nonlinear Spinor Field Equations Depending on the Invariant Function <i>I<sub>P</sub></i>=<i>P</i><sup>2</sup>in the General Relativity Theory

作     者：A.Adomou Jonas Edou Siaka Massou 

作者机构：Department of Theoretical Physics and MathematicsUniversity of Abomey-CalaviAbomey-CalaviBenin National Superior Institute of Industrial TechnologyINSTI-LokossaNational University of SciencesTechnologyEngineering and Mathematics of AbomeyAbomeyBenin 

出 版 物：《Journal of Applied Mathematics and Physics》 (应用数学与应用物理（英文）)

年 卷 期：2019年第7卷第11期

页      面：2818-2835页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Lagrangian Spherical Symmetric Metric Soliton-Like Solution 

摘      要：The present research work is considered as part II of the previous work entitled [Plane Symmetric Solutions to the Nonlinear Spinor Field Equations in General Relativity Theory, jmp, 2019, 10, 1222-1234]. Here, we opt for the static spherical symmetric metric. In this metric, we have obtained spherical symmetric soliton-like solutions to the spinor field equations with nonlinear terms, which are arbitrary functions of , taking into account the proper gravitational field of elementary particles. Equations with power and polynomial nonlinearities are investigated in detail. It is shown that the initial set of the Einstein and spinor field equations with a power-law nonlinearity possess regular solutions with a localized energy density of the spinor field only if we consider massless particle without losing the generality (m = 0). In this case, a soliton-like configuration has negative energy. In order to define the role of the nonlinearity and the own gravitational field of the elementary particles in this model, we have obtained exact static symmetric solutions to the above spinor field equations in the linear case by considering Dirac’s equations and in flat space-time. It is proved that soliton-like solutions are absent in the linear case. But in flat space-time soliton-like configurations exist and have positive total energy.