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arXiv · 1305.4073

A Generalized Family of Post-Newtonian Dedekind Ellipsoids

Norman Gürlebeck·David Petroff
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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.

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Norman Gürlebeck, David Petroff. 2013-05-17. A Generalized Family of Post-Newtonian Dedekind Ellipsoids. https://doi.org/10.1088/0004-637x/777/1/60

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