Wormholes with matter haunted by conformally coupled ghosts

In this work, we present novel analytical solutions for static and spherically symmetric wormhole geometries threaded by an anisotropic distribution of matter conformally coupled to a scalar ghost field. We explore the main features of the theory, such as the dynamics of the scalar field and matter throughout the wormhole, as well as the role played by the non-minimal coupling. Furthermore, coupled ghosts in the presence of a scalar potential are considered and traversability conditions are analysed within such geometrical scheme. More specifically, we find analytical solutions that although the energy density of the ghost is strictly negative, the energy density of matter may attain positive values.