Mixed star-plus-wormhole systems with a complex scalar field

Abstract

We study compact mixed configurations with a nontrivial wormholelike spacetime topology supported by a complex ghost scalar field with a quartic self-interaction and a polytropic fluid. The latter is modeled by a relativistic barotropic equation of state that can approximately describe more or less realistic matter. For such systems, we find regular asymptotically flat equilibrium solutions describing localized configurations in which the fluid is concentrated in a finite-size region. The solutions obtained describe double-throat wormholes which are located outside the fluid (one can say that the fluid is hidden inside the region between the throats). Also, we consider the dependence of the total mass of the system on the central density of the fluid and demonstrate the existence of critical values of the central density at which the mass diverges. In this case all regular solutions possessing finite masses lie in the region between these critical values, and this region also contains a discontinuity in magnitudes of the central density where only physically unacceptable oscillating solutions do exist. Is shown that for some values of the central density of the fluid there can exist solutions describing systems whose fluid density and pressure maxima lie not at the center. This results in the fact that such systems possess two equators (local maxima of the metric function) resided symmetrically with respect to the center.