Nonlinear spinor fields in Bianchi-I space: Exact self-consistent solutions

Abstract

Calculations are performed to obtain exact self-consistent solutions of nonlinear spinor-field equations with self-action terms in Bianchi-I space. The latter terms are arbitrary functions of the invariant\(s = \overline \psi \psi \). A detailed examination is made of equations with exponential nonlinearity, when the nonlinear term in the Lagrangian of the spinor field Ln=λsn. Here, λ is the nonlinearity parameter, n>1. It is shown that these equations have finite solutions and solutions that are singular at the initial moment of time. The singularity is absent in the case of solutions that describe systems of fields for which the energy dominance condition is violated. It is further shown that if the mass parameter m≠0 in the spinor-field equation, expansion of Bianchi-I space becomes isotropic as t → ∞. This does not occur when m=0. Specific examples of solutions of linear and nonlinear spinor-field equations are presented.