A Remark on the Geometry of Uniformly Rotating Stars

TL;DR

This paper classifies the geometric properties of equilibrium shapes of uniformly rotating, self-gravitating fluid stars, especially white dwarfs, by analyzing critical points of a related functional.

Contribution

It provides a classification of the free boundary configurations for rotating fluid masses, extending to models with prescribed angular momentum.

Findings

Classified equilibrium configurations of rotating fluid masses.

Applicable to models with prescribed angular momentum.

Provides insights into the geometry of rotating white dwarf stars.

Abstract

In this paper we classify the free boundary associated to equilibrium configurations of compressible, self-gravitating fluid masses, rotating with constant angular velocity. The equilibrium configurations are all critical points of an associated functional and not necessarily minimizers. Our methods also apply to alternative models in the literature where the angular momentum per unit mass is prescribed. The typical physical model our results apply to is that of uniformly rotating white dwarf stars.