Composite vacuum Brans-Dicke wormholes

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 \(\omega\), however they are described by the Brans class I solution with different sets of parameters of integration. In particular, the exterior vacuum solution has \(C_{ext}(\omega)\equiv 0\). In this case the Brans class I solution for any \(\omega\) 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 \(C_{int}(\omega)=-1/(\omega+2)\). In this case the Brans class I solution describes a wormhole spacetime provided \(\omega\) lies in the narrow interval \(-2-\frac{\sqrt{3}}{3}