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

Jose D. Polanco·Patricio S. Letelier·Maximiliano Ujevic
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Abstract

A numerical solution of Einstein field equations for a spherical symmetric and stationary system of identical and auto-gravitating particles in phase transition is presented. The fluid possess 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 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.

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Jose D. Polanco, Patricio S. Letelier, Maximiliano Ujevic. 2004-08-05. Space-Time geometry and thermodynamic properties of a self-gravitating ball of fluid in phase transition. https://doi.org/10.1103/physrevd.70.064006

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