# Rapidly Rotating White Dwarfs

## TL;DR

This paper proves the existence of rapidly rotating white dwarf star models using the Euler-Poisson system, showing how their properties change with increasing rotation speed.

## Contribution

It introduces a new existence theorem for rapidly rotating white dwarfs with continuous dependence on rotation speed, using global continuation and limiting processes.

## Key findings

- Solutions form a connected set in function space
- Supports or densities become unbounded with increased rotation
- Discussion of the polytropic case with critical exponent b3=4/3

## Abstract

A rotating star may be modeled as a continuous system of particles attracted to each other by gravity and with a given total mass and prescribed angular velocity. Mathematically this leads to the Euler-Poisson system. A white dwarf star is modeled by a very particular, and rather delicate, equation of state for the pressure as a function of the density. We prove an existence theorem for rapidly rotating white dwarfs that depend continuously on the speed of rotation. The key tool is global continuation theory, combined with a delicate limiting process. The solutions form a connected set $\mathcal K$ in an appropriate function space. As the speed of rotation increases, we prove that either the supports of white dwarfs in $\mathcal K$ become unbounded or their densities become unbounded. We also discuss the polytropic case with the critical exponent $\gamma=4/3$.