Exact solutions of Brans–Dicke theory for irrotational barotropic models with stiff matter

In the previous work, we have obtained classes of exact solutions of Brans–Dicke (BD) theory when only a scalar field is present and also in the presence of an electromagnetic field. In the present paper, we have generated a new class of solutions of BD theory corresponding to irrotational barotropic perfect fluid with pressure equal to energy density. The main result of the paper may be stated as follows: ’’Corresponding to any diagonalizable solution of Einstein vacuum field equations, in which fields and metric tensors are functions of not more than three variables, we can generate a solution of the Brans–Dicke theory for the irrotational barotropic perfect fluid with pressure equal to energy density.’’