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A new numerical method for computing the structure of rapidly rotating fluid bodies in general relativity is presented. The method is a Henyey-type relaxation method of the kind previously used by Stoeckly in Newtonian theory. It permits the construction of accurate models for fluid bodies with various strengths of relativity and various amounts of uniform or differential rotation. The method is used to construct sequences of uniformly rotating homogeneous bodies, the relativistic analogs of the classical Maclaurin spheroids. The results reveal that, in contrast to the Newtonian sequence, most, and probably all, of the relativistic sequences terminate at nonzero ratios of proper polar radius to proper equatorial radius where centrifugal and gravitational accelerations balance at the equator. Other relativistic effects, including those associated with the formation of regions within which observers must rotate relative to infinity, are discussed. The computational results provide a foundation for a speculative discussion of stability and a scenario for the possible evolution of contracting bodies. Emerging from this are suggestions that relativistic effects might channel the contraction of a highly relativistic body toward a nearly spherical, rather than a disklike, configuration, and that black holes might generally not be near the extreme Kerr limit when they initially form. The computational results are also applied to uniformly rotating neutron stars in order to obtain rough estimates of their rotational energies, their moments of inertia, and the percent by which uniform rotation can increase the maximummass limit above its nonrotating value. For equations of state yielding a maximum mass 1.3 M0 in the nonrotating limit, this latter percent increase is estimated to be 15 percent if attention is restricted to completely stable objects and 30 percent if no stability restrictions are imposed. Subject headings: relativity - rotation - stars: collapsed
Butterworth et al. (Sun,) studied this question.