General Relativistic Stars: Linear Equations of State

TL;DR

This paper reformulates Einstein's equations for static, spherically symmetric stars with linear equations of state into a dynamical system, analyzing their structure qualitatively and numerically to understand solution behaviors.

Contribution

It introduces a novel dynamical systems approach to analyze Einstein's equations for such stars, identifying key solutions that shape the overall solution structure.

Findings

Special solutions act as fundamental building blocks.

The approach applies to more general barotropic equations.

Insights into solution features with high central pressure.

Abstract

In this paper Einstein's field equations, for static spherically symmetric perfect fluid models with a linear barotropic equation of state, are recast into a 3-dimensional regular system of ordinary differential equations on a compact state space. The system is analyzed qualitatively, using the theory of dynamical systems, and numerically. It is shown that certain special solutions play important roles as building blocks for the solution structure in general. In particular, these special solutions determine many of the features exhibited by solutions with a regular center and large central pressure. It is also shown that the present approach can be applied to more general classes of barotropic equations of state.