Nonlinear Dirac equation in two-spinor form: Separation in static RW space-time

Abstract

The Dirac equation with nonlinear terms induced by torsion is studied in Robertson-Walker (RW) space-time. An extension of a separation method of the equation, based on the Newman-Penrose formalism and previously applied to the nonlinear case, is considered. Accordingly the angular dependence of the Dirac spinor solution is separated, under a special assumption, in the general time-dependent RW metric. In the case of static RW metric the time dependence of the Dirac spinor factors out and one is left with a pair of two coupled nonlinear radial equations. The radial equations are disentangled by a suitable substitution of the spinor solution. The problem amounts then to the solution of a single second-order highly nonlinear differential equation. Some elementary considerations are done on the asymptotic behavior of the solution of the equation.