On Rotating Axisymmetric Solutions of the Euler-Poisson Equations

Abstract

We consider stationary axisymmetric solutions of the Euler-Poisson equations, which govern the internal structure of barotropic gaseous stars. We take the general form of the equation of states which cover polytropic gaseous stars indexed by $6/5<\gamma <2$ and also white dwarfs. A generic condition of the existence of stationary solutions with differential rotation is given, and the existence of slowly rotating configurations near spherically symmetric equilibria is shown. The problem is formulated as a nonlinear integral equation, and is solved by an application of the infinite dimensional implicit function theorem. Oblateness of star surface is shown and also relationship between the central density and the total mass is given.

Typos have been corrected

References in corpus (2)

• Existence and Nonlinear Stability of Rotating Star Solutions of the Compressible Euler-Poisson Equations
• On slowly rotating axisymmetric solutions of the Euler-Poisson equations

Cited by in corpus (8)

• Linearized Analysis of Barotropic Perturbations around Spherically Symmetric Gaseous Stars Governed by the Euler-Poisson Equations
• On slowly rotating axisymmetric solutions of the Einstein-Euler equations
• Stability of rotating gaseous stars
• Existence and uniqueness of compact rotating configurations in GR in second order perturbation theory
• On the axisymmetric metric generated by a rotating perfect fluid with the vacuum boundary
• A Remark on the Matter-Vacuum Matching Problem for Axisymmetric Metrics Governed by the Einstein-Euler Equations
• Steady States of Rotating Stars and Galaxies
• Existence of Rotating Stars with Variable Entropy