General class of vacuum Brans-Dicke wormholes

Recently, traversable wormhole geometries were constructed in the context of f(R) gravity. The latter is equivalent to a Brans-Dicke theory with a coupling parameter w=0, which is apparently excluded from the narrow interval, -3/2<w<-4/3, extensively considered in the literature of static wormhole solutions in vacuum Brans-Dicke theory. However, this latter interval is only valid for a specific choice of an integration constant of the field equations derived on the basis of a post-Newtonian weak field approximation, and there is no reason for it to hold in the presence of compact objects with strong gravitational fields. In this context, we construct a general class of vacuum Brans-Dicke wormholes that include the value of w=0. Furthermore, we present the general condition for the existence of vacuum Brans-Dicke wormhole geometries, and show that the presence of effective negative energy densities is a generic feature of these vacuum solutions.