  When dealing with a spacetime, one usually searches for singularities, black
holes, white holes and wormholes due to their importance to the motion of
particles. There is a family of solution of the Brans-Dicke vacuum equations
that has not been fully studied from this perspective. In this paper, I study
some properties of this family and find the complete set of solutions that
avoids singularity at the point where the metric diverges or degenerates. The
possible changes in the metric signature when passing through this point is
analyzed. In addition, I also study the radial geodesics and obtain the
solutions of some particular cases.
