Soliton of Self-Consistent System of Nonlinear Spinor and Gravitational Fields With the Arbi- Trary Function Depending on the Bilinear Pauli- Fierz Invariant Is = S2 in General Relativity

Abstract

A self-consistent system of nonlinear spinor and gravitational fields, modeled by static spherical symmetric metric, is considered and studied. Exact spherical symmetric solutions of nonlinear spinor field equations in the Gravitational Theory are obtained. The nonlinearity in the spinor lagrangian is given by an arbitrary function which depends on the invariant generated from the Fierz-Pauli bilinear spinor form IS = S2. It is shown that a soliton-like configuration has a localized energy density and a finite total energy. In addition, The total charge and total spin are also finite. Let us emphasize that the effect of gravitational field on the properties of regular localized solutions significantly depends on the symmetry of the system. The nonlin- ear terms, the gravitational field of elementary particles and the geometrical properties of the metric of the space-time play an important role in the obtaining of analytical solutions having the soliton-like configuration. Let us emphasize that the numerical solutions of the solutions obtained here are presented in graphical form.