The PostNewtonian Effects of General Relativity on the Equilibrium of Uniformly Rotating Bodies. III. The Deformed Figures of the Jacobi Ellipsoids
Abstract
The effects of general relativity, in the postNewtonian approximation, on the Jacobian figures of equilibrium of uniformly rotating homogeneous masses are determined. It is shown, for example, that the postNewtonian figure is obtained by a deformation of the Jacobi ellipsoid by a suitable Lagrangian displacement cubic in the coordinates. The solution of the postNewtonian equations exhibits an indeterminacy at the point of bifurcation M2, where the Jacobian sequence branches off from the Maclaurin sequence, and a singularity at a point J4, where the axes of the Jacobi ellipsoid are in the ratios 1:0 2972:0.2575. The indeterminacy in the solution at M2 arises from the fact that at this point the Maclaurin spheroid is neutral to an infinitesimal deformation proportional to (s , x2, 0); and the singularity at J4 arises from the fact that at this point the Jacobi ellipsoid is unstable to the deformation induced by the effects of general relativity.
 Publication:

The Astrophysical Journal
 Pub Date:
 May 1967
 DOI:
 10.1086/149183
 Bibcode:
 1967ApJ...148..621C