Solution generating in scalar-tensor theories with a massless scalar field and stiff perfect fluid as a source

We present a method for generating solutions in some scalar-tensor theories with a minimally coupled massless scalar field or irrotational stiff perfect fluid as a source. The method is based on the group of symmetries of the dilaton-matter sector in the Einstein frame. In the case of Barker's theory the dilaton-matter sector possesses the SU(2) group of symmetries. In the case of Brans-Dicke theory and the theory with "conformal coupling," the dilaton-matter sector has SL(2,R) as a group of symmetries. We describe an explicit algorithm for generating exact scalar-tensor solutions from solutions of Einstein minimally coupled scalar field equations by employing the nonlinear action of the symmetry group of the dilaton-matter sector. In the general case, when the Einstein frame dilaton-matter sector may not possess nontrivial symmetries, we also present a solution generating technique which allows us to construct exact scalar-tensor solutions starting with the solutions of the Einstein minimally coupled scalar field equations. As an illustration of the general techniques, examples of explicit exact solutions are constructed. In particular, we construct inhomogeneous cosmological scalar-tensor solutions whose curvature invariants are everywhere regular in space-time. A generalization of the method for scalar-tensor-Maxwell gravity is outlined.