A fundamental ingredient in wormhole physics is the presence of exotic matter, which involves the violation of the null energy condition. Although a plethora of wormhole solutions have been explored in the literature, it is useful to find geometries that minimize the usage of exotic matter. In this work, we find exact wormhole solutions in Brans–Dicke theory where the normal matter threading the wormhole satisfies the null energy condition throughout the geometry. Thus, the latter implies that it is the effective stress–energy tensor containing the scalar field, that plays the role of exotic matter, that is responsible for sustaining the wormhole geometry. More specifically, we consider a zero redshift function and a particular choice for the scalar field and determine the remaining quantities, namely, the stress–energy tensor components and the shape function. The solution found is not asymptotically flat, so that this interior wormhole spacetime needs to be matched to an exterior vacuum solution.
Vacuum polarization of the quantized massive scalar field in the global monopole spacetime: The renormalized quantum stress energy tensor
