Traversable wormholes induced by stress energy conservation: combining Casimir energy with a scalar field

We investigate possible manifolds characterizing traversable wormholes in the presence of a scalar field minimally coupled to gravity, which has both kinetic and potential energy. The feature of traversability requires the violation of the null energy condition, which, in turn, signals the existence of exotic matter with negative energy density. To achieve this, we introduce a hypothetical Casimir apparatus with plates positioned either at a parametrically fixed or radially varying distance. A consistent set of field equations requires the introduction of an auxiliary field composed solely of pressure terms, which we interpret as the gravitational back-reaction of the traversable wormhole to the original source. Interestingly, the only case that appears to avoid the need for such an auxiliary field involves a scalar field with potential energy, combined with a Casimir device with fixed plates.