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Space-time geometry and thermodynamic properties of a self-gravitating ball of fluid in phase transition

A numerical solution of Einstein field equations for a spherical symmetric and stationary system of identical and autogravitating particles in phase transition is presented. The fluid possesses a perfect fluid energy-momentum tensor, and the internal interactions of the system are represented by a van der Walls-like equation of state, able to describe a first order phase transition of the type gas-liquid. We find that the space-time curvature, the radial component of the metric, and the pressure and density show discontinuities in their radial derivatives in the phase coexistence region. This region is found to be a spherical surface concentric with the star, and the system can be thought of as a foliation of acronal, concentric and isobaric surfaces in which the coexistence of phases occurs in only one of these surfaces. This kind of system can be used to represent a star with a high energy density core and low energy density mantle in hydrodynamic equilibrium.