The Axisymmetric Case for the Post-Newtonian Dedekind Ellipsoids

TL;DR

This paper extends previous work on post-Newtonian Dedekind ellipsoids to include axisymmetric cases, addressing limitations in earlier models that excluded uniformly rotating spheroids in this limit.

Contribution

It introduces a modified approach that allows for the existence of axisymmetric solutions in the post-Newtonian approximation, overcoming previous restrictions.

Findings

Demonstrates the existence of axisymmetric solutions in the post-Newtonian framework.

Extends Chandrasekhar & Elbert's method to include axisymmetric limits.

Provides a more complete understanding of Dedekind ellipsoids in relativistic regimes.

Abstract

We consider the post-Newtonian approximation for the Dedekind ellipsoids in the case of axisymmetry. The approach taken by Chandrasekhar & Elbert (1974, 1978) excludes the possibility of finding a uniformly rotating (deformed) spheroid in the axially symmetric limit, though the solution exists at the point of axisymmetry. We consider an extension to their work that permits the possibility of such a limit.