An anisotropic model for coupled electromagnetic and scalar fields

An attempt is made to solve the Einstein's field equations with cylindrical symmetry, imposing some restrictions on electromagnetic fields. A theorem is established in order to generate this set of solutions from those of electrovac field equations without solving the highly nonlinear field equations. The relativistic field equations for coupled electromagnetic and massless scalar field are examined. The field equations are solved for the case M=ψ2=0 and N=ψ3=N(r), where ψi denote electromagnetic four potential. Two particular cases of solutions are discussed