Phase Transitions and the Mass-Radius Curves of Relativistic Stars

TL;DR

This paper analyzes how first-order phase transitions in the equation of state affect the mass-radius curves of relativistic stars, revealing conditions for cusps and singularities in these curves.

Contribution

It provides analytical descriptions of mass-radius curves with phase transitions, highlighting the effects of density discontinuities on curve features.

Findings

Mass-radius curve slope is continuous except at specific density discontinuities.

Cusps form in the curve when the density discontinuity exceeds a critical value.

Singular curvature occurs where high-density phase first appears.

Abstract

The properties of the mass-radius curves of relativistic stellar models constructed from an equation of state with a first-order phase transition are examined. It is shown that the slope of the mass-radius curve is continuous unless the discontinuity in the density at the phase transition point has a certain special value. The curve has a cusp if the discontinuity is larger than this value. The curvature of the mass-radius curve becomes singular at the point where the high density phase material first appears. This singularity makes the mass-radius curve appear on large scales to have a discontinuity in its slope at this point, even though the slope is in fact continuous on microscopic scales. Analytical formulae describing the behavior of these curves are found for the simple case of models with two-zone uniform-density equations of state.