Another Equilibrium Sequence of Self-Gravitating and Rotating Incompressible Fluid

Abstract

A new sequence of gravitational equilibria was obtained for uniformly rotating ax· isymmetric incompressible fluid. This sequence parts from the Maclaurin sequence at the neutral point against the P.(r;) displacement at the surface. It continues into a concave hamburger-like shape, and finally into a toroid. Therefore, this neutral point on the Maclaurin sequence is one of the points of bifurcation. § 1. Introduction It has been said that there are only two axisymmetric equilibrium sequences in the case of self-gravitating, uniformly rotating incompressible fluids-Mac-laurin spheroids l) and Dyson-Wong toroids. 2) In the study of post-Newtonian effects on the structure of the Maclaurin spheroids, Chandrasekhar 3) and Bar-deen 4) have shown that there is a neutral point on the Maclaurin sequence against the perturbation of P4(7J) displacement at the surface where 7J is one of the spheroidal coordinates. The neutral point corresponds to the eccentricity of the spheroidal configuration e= ecr=0.98523. Bardeen 4) has also proved that non-spheroidal configurations can be in gravitational equilibrium so far as the first-order deformation from the Maclaurin spheroid is