Generation of solutions of the interior Brans-Dicke equations

Given any solution of Einstein's equation for a static perfect fluid, with pressure proportional to energy density, it is shown how a corresponding solution of the Brans-Dicke equation can be constructed. For asymptotically flat spaces, with suitable continuity properties, the converse is also true. As an illustration of this method we obtain the Brans-Dicke solution that corresponds to the well-known exact solution to the Oppenheimer-Volkoff equation for the case of infinite central density.