Rapidly rotating fluid bodies in general relativity

Abstract

A self-consistent-field method is developed for numerically constructing rapidly rotating fluid bodies in general relativity. Results which emerge from using it to build uniformly rotating homogeneous bodies are discussed. The results reveal that, in contrast to the Newtonian sequence of Maclaurin spheroids, the relativistic sequences in most, and probably all, cases terminate at eccentricities less than 1, where the centrifugal and gravitational accelerations at the equator become equal. The results also suggest that a highly relativistic rotating body, due to certain effects, might evolve toward a nearly spherical configuration as it contracts.