On the spherical symmetry of static stellar models

Abstract

This paper completes the proof of the necessity of spherical symmetry in the static general-relativistic stellar models that have equations of state satisfying certain inequalities. The technical assumption — that there exists a “reference spherical stellar model” — that was essential in the previous discussions of this problem is removed. This paper also extends beyond previous discussions the class of equations of state included in the proof. The analysis of the equations for spherical stellar models, used here to demonstrate the existence of a “reference spherical model,” may also be of independent interest.