A GENERALIZED FAMILY OF POST-NEWTONIAN DEDEKIND ELLIPSOIDS

Article

A GENERALIZED FAMILY OF POST-NEWTONIAN DEDEKIND ELLIPSOIDS

Gurlebeck, N.; Petroff, D.

ApJ, 777-60 (2013)

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.

Keywords

gravitation – relativistic processes – stars: general – stars: kinematics and dynamics – stars: neutron

BibTeX

@article{UTF529,
  author        = {Gurlebeck, N. and Petroff, D.},
  title         = {{A GENERALIZED FAMILY OF POST-NEWTONIAN DEDEKIND ELLIPSOIDS}},
  journal       = {ApJ},
  pages         = {777-60},
  year          = {2013},
  doi           = {10.1088/0004-637X/777/1/60},
}