A Generalized Family of Post-Newtonian Dedekind Ellipsoids
Abstract
We derive a family of Post-Newtonian (PN) Dedekind ellipsoids to first order. They describe non-axially symmetric, homogeneous, and rotating figures of equilibrium. The sequence of the Newtonian Dedekind ellipsoids allows for an axially symmetric limit in which a uniformly rotating Maclaurin spheroid is recovered. However, the approach taken by Chandrasekhar & Elbert (1974) to find the PN Dedekind ellipsoids excludes such a limit. In G\"urlebeck & Petroff (2010), we considered an extension to their work that permits a limit of 1 PN Maclaurin ellipsoids. Here we further detail the sequence and demonstrate that a choice of parameters exists with which the singularity formerly found in Chandrasekhar & Elbert (1974) along the sequence of PN Dedekind ellipsoids is removed.
Keywords
Cite
@article{arxiv.1305.4073,
title = {A Generalized Family of Post-Newtonian Dedekind Ellipsoids},
author = {Norman Gürlebeck and David Petroff},
journal= {arXiv preprint arXiv:1305.4073},
year = {2013}
}
Comments
23 pages, 17 figures; changes in v2: first paragraph in introduction added, minor changes to agree with published version