The present research work deals with an extension of a previous work entitled [Exact Soliton-like spherical symmetric solutions of the Heisenberg-Ivanenko type nonlinear spinor field equation in gravitational theory, ...The present research work deals with an extension of a previous work entitled [Exact Soliton-like spherical symmetric solutions of the Heisenberg-Ivanenko type nonlinear spinor field equation in gravitational theory, Journal of Applied Mathematics and Physics, 2020, 8, 1236-1254] to Analytical Soliton-Like Solutions to Nonlinear Dirac Equation of Spinor Field in Spherical Symmetric Metric. The nonlinear terms in the Lagrangian density are functions of the invariant <img src="Edit_f8bf864e-8dfd-42d9-82fc-76b8c18997cc.png" alt="" />. Equations with power and polynomial nonlinearities are thoroughly scrutinized. It is shown that soliton is responsible for the deformation in the metric and hence in the geometry as well as gravitational field. The role of nonlinearity and the influence of the proper gravitational field of the elementary particles are also examined. The consideration of the nonlinear terms in the spinor Lagrangian, the own gravitational field of elementary particles and the geometrical properties of the metric are necessary and sufficient conditions in order to obtain soliton-like solutions with total charge and total spin in general relativity.展开更多
文摘The present research work deals with an extension of a previous work entitled [Exact Soliton-like spherical symmetric solutions of the Heisenberg-Ivanenko type nonlinear spinor field equation in gravitational theory, Journal of Applied Mathematics and Physics, 2020, 8, 1236-1254] to Analytical Soliton-Like Solutions to Nonlinear Dirac Equation of Spinor Field in Spherical Symmetric Metric. The nonlinear terms in the Lagrangian density are functions of the invariant <img src="Edit_f8bf864e-8dfd-42d9-82fc-76b8c18997cc.png" alt="" />. Equations with power and polynomial nonlinearities are thoroughly scrutinized. It is shown that soliton is responsible for the deformation in the metric and hence in the geometry as well as gravitational field. The role of nonlinearity and the influence of the proper gravitational field of the elementary particles are also examined. The consideration of the nonlinear terms in the spinor Lagrangian, the own gravitational field of elementary particles and the geometrical properties of the metric are necessary and sufficient conditions in order to obtain soliton-like solutions with total charge and total spin in general relativity.
