#### Bulg. J. Phys. vol.30 no.3-4 (2003), pp. 089-112

#### Exact Self-Consistent Plane-Symmetric Solutions to the Spinor and Scalar Field Equations

B. Saha

go back^{}, G.N. Shikin^{}*Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna 141980 Dubna, Moscow region, Russia*Abstract.We consider a system of nonlinear spinor and scalar fields with minimal coupling in general relativity. The nonlinearity in the spinor field Lagrangian is given by an arbitrary function of the invariants generated from the bilinear spinor formsS=ψψ andP= iψγ^{5}ψ; the scalar Lagrangian is chosen as an arbitrary function of the scalar invariant Ω=&phi\sub>,αφ^{,α}, that becomes linear at Ω→0. The spinor and the scalar fields in question interact with each other by means of a gravitational field which is given by a plane-symmetric metric. Exact plane-symmetric solutions to the gravitational, spinor and scalar field equations are obtained. Spinor field equations with the nonlinear term being a power function ofI, i.e.,L= λ_{N}I, where^{n}I = S, P^{2}, orS^{2}±P^{2}, λ is the self-coupling constant andnis the power of nonlinearity, are thoroughly investigated. Role of gravitational field in the formation of the field configurations with limited total energy, spin and charge has been investigated. Influence of the change of the sign of energy density of the spinor and scalar fields on the properties of the configurations obtained has been examined. It has been established that under the change of the sign of the scalar field energy density the system in question can be realized physically iff the scalar charge does not exceed some critical value. In case of spinor field no such restriction on its parameter occurs. In general it has been shown that the choice of spinor field nonlinearity can lead to the elimination of scalar field contribution to the metric functions, but leaving its contribution to the total energy unaltered.