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

TL;DR

This paper presents a numerical analysis of a self-gravitating fluid sphere undergoing phase transition, revealing discontinuities in space-time and matter properties, modeling a star with a high-density core and low-density mantle.

Contribution

It introduces a novel numerical solution for Einstein equations with a van der Waals-like equation of state, capturing phase transition effects in self-gravitating fluids.

Findings

Discontinuities in curvature, pressure, and density derivatives at the phase boundary.

The phase coexistence region forms a spherical surface within the star.

The model can represent stars with distinct core and mantle energy densities.

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.