Spherical Symmetric Kink-Like Configurations of Spinor and Gravitational Fields

Abstract

The present research work deals with an extension of a previous work [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 Spherical Symmetric Kink-Like Configurations of Spinor and Gravitational Fields. We have obtained exact kink-like static spherical symmetric solutions to the self-consistent system of spinor and gravitational fields equations. The Einstein’s field equation shave been solved by the Liouville method. The principal difference between kink soliton with antikink soliton has been established. The nonlinear terms in the lagrangian are arbitrary functions F(IS) depending on the invariant IS = S2= ( )2. It is shown that the initial set of the Einstein and spinor field equations have regular solutions with a localized energy density of the spinor field only if m = 0 (m is the mass parameter in the spinor field equations). Equations with polynomial nonlinearities are thoroughly scrutinized. Let us emphasize that the spinor field with polynomial nonlinearities has a regular solutions with localized, positive and alternating energy density and finite total energy. In addition, the total charge and the total spin are also finte. We have also obtained exact solutions to the linear spinor field equations. We remarked that in this case soliton-like solutions are absent. Furthermore, we note that the properties of regular localized solutions depend on the symmetry and the nonlinear terms in the lagrangian of the self-consistent system of gravitational and spinor fields.