Nonlinear spinor in a Kerr–Schild background

Abstract

We study the nonlinear spinor field in a Kerr–Schild background by first looking for solitonic solutions in the absence of rotation, given that in the special relativistic limit there are solitonic solutions in this approximation. Since for the scalar field problem at least two independent radial functions are needed for the solitonic solutions to exist, we introduce a dilation field by deforming the Kerr–Schild metric by a Weyl factor. We find that for the parameter space studied there are no solitonic solutions in the spherically symmetric approximation. While in the present work we have studied the spinor field, we also had in mind a corresponding study of a scalar field in the same background where it may be of interest for describing a rotating stellar soliton. The proposed strategy in both cases begins by looking for solitonic solutions in the absence of rotation and then continues by perturbatively correcting for the rotation required by the angular dependence of the Kerr background. The strategy appears to be unsuccessful.