Abstract
Abstract We study configurations consisting of a gravitating linear spinor field and a massless ghost scalar field providing a nontrivial spacetime topology. For such a mixed system, we have constructed two families of asymptotically flat asymmetric solutions describing localized configurations (Dirac stars) possessing a wormhole topology. The physical properties of such systems are completely determined by the values of the spinor frequency and the throat parameter. For a fixed value of the latter, we have compared mass curves for the two families of solutions and revealed considerable differences in their behavior and physical properties of the systems under consideration (the configurations may be regular or singular and possess one or two throats, as well as they may contain possible event horizons).