Non linear spin 1 field equation in curved space-time: separation and solution in static RW metric

Abstract

A non linear spin 1 field equation is proposed in a general curved space time. The non-linearity is represented by a reduced version of a torsion induced non linearity previously considered. The field equation is made explicit in the Robertson Walker space-time by means of the Newman Penrose formalism based on a given null tetrad frame. In case of static space time and time oscillating field, the angular and radial dependence are separated with a separation formalism borrowed from the linear case. By suitable assumption the separated angular equations are integrated and there esults a cylindrical symmetry of the solutions. The radial dependence is reduced to the study of two coupled non linear radial equations. The solution is finally reported to the solution of a Bernoulli equation that is studied in every case of the curvature parameter.