"Jordan's Scalar Stars" and Dark Matter

Here we are starting the study of the field equations of relativistic scalar tensor theories in the spherically symmetric gravitational field. In the present article we shall consider as an example only the simplest Jordan-Brans-Dicke (JBD) one. To illustrate the property of the spherically symmetric JBD configuration we exhibit a new representation of the well-known four dimensional solutions. In this model, a suitable segment of Brans solution is chosen for the interior of the object while the outer region consists of a Schwarzschild vacuum. We have constructed "Jordan's scalar stars" model consisting of three parts: a homogeneous inner core with linear equation of state; an envelope of Brans spacetime matching the core and the exterior Schwarzschild spacetime. We have also showed that this toy model can explain the intergalactic effects without the dark matter hypothesis.