Composite vacuum Brans-Dicke wormholes

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We construct a new static spherically symmetric configuration composed of interior and exterior Brans-Dicke vacua matched at a thin matter shell. Both vacua correspond to the same Brans-Dicke coupling parameter ω, however they are described by the Brans class I solution with different sets of parameters of integration. In particular, the exterior vacuum solution has Cext(ω)≡ 0. In this case the Brans class I solution for any ω reduces to the Schwarzschild one being consistent with restrictions on the post-Newtonian parameters following from recent Cassini data. The interior region possesses a strong gravitational field, and so the interior vacuum solution has Cint(ω)=-1/(ω+2). In this case the Brans class I solution describes a wormhole spacetime provided ω lies in the narrow interval -2-√33<ω<-2. The interior and exterior regions are matched at a thin shell made from an ordinary perfect fluid with positive energy density and pressure obeying the barotropic equation of state p=kσ with 0≤ k≤1. The resulting configuration represents a composite wormhole, i.e. the thin matter shell with the Schwarzschild-like exterior region and the interior region containing the wormhole throat.