Within the framework of the scalar-tensor models of gravitation and by
relying on analytical and numerical techniques, we establish the existence of a
class of spherically symmetric spacetimes containing a naked singularity. Our
result relies on and extends a work by Christodoulou on the existence of naked
singularities for the Einstein-scalar field equations. We establish that a key
parameter in Christodoulou's construction couples to the Brans-Dicke field and
becomes a dynamical variable, which enlarges and modifies the phase space of
solutions. We recover analytically many properties first identified by
Christodoulou, in particular the loss of regularity (especially at the center),
and then investigate numerically the properties of these spacetimes.Comment: 26 pages, PACS numbers: 04.20.Dw, 04.25.dc, 04.50.K
