Exact static solutions of nonlinear equations of a spinor field in the Gödel universe

Summary (translated from the Russian): "We obtain exact static solutions of spinor field equations with nonlinear terms that are arbitrary functions of the invariant S=obar psi psi in the external gravitational field of the Gödel universe. We consider a specific type of nonlinear Lagrangian that leads to a regular and localized distribution of the spinor field energy density. We also obtain exact solutions of the original equations in flat space-time. Here we show that irrespective of the form of the nonlinear Lagrangian, the energy density of the spinor field is a constant quantity, i.e., there is no localization. This means that the external gravitational field of the Gödel universe plays a decisive role in the formation of soliton-like configurations of the nonlinear spinor field."