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 to find the PN Dedekind ellipsoids excludes such a limit.
In a previous work, 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 by Chandrasekhar & Elbert along the sequence of PN Dedekind ellipsoids is removed.