Nonlinear Spinor Field Equation of the Bilinear Pauli-Fierz Invariant Iv = S2 + P2: Exact Spherical Symmetric Soliton-Like Solutions in General Relativity

Taking into account the own gravitational field of elementary particles, we have obtained exact static spherical symmetric
solutions to the spinor field equation. The nonlinear terms LN are arbitrary functions of bilinear Pauli-Fierz invariant
Iv = S2 + P2. It characterizes the self-interaction of a spinor field. We have investigated in detail equations with power
and polynomial nonlinearities. The spinor field equation with a power-law nonlinearity have regular solutions with a
localized energy density and regular metric. In this case a soliton-like configuration has finite and negative total energy.
As for equations with polynomial nonlinearity, the obtained solutions are regular with a localized energy density and
regular metric but its total energy is finite and positive.