On a criterion for the occurrence of a Dedekind-like point of bifurcation along a sequence of axisymmetric systems. I. Relativistic theory of uniformly rotating configurations

Abstract

Stationary nonaxisymmetric systems in general relativity are considered. It is shown that the theory of such systems can be developed along lines which closely parallel the theory of nonstationary axisymmetric systems. Equations are derived which govern small nonaxisymmetric departures from equilibrium of axisymmetric configurations of perfect fluid in uniform rotation. In terms of these equations, the condition that a uniformly rotating configuration will allow a quasi-stationary nonaxisymmetric deformation with a Φ-dependence of the form e^imΦ (where m is an integer greater than or equal to one) is obtained. A variational principle expressing this condition is also derived.