On the Stability of Axisymmetric Systems to Axisymmetric Perturbations in General Relativity. II. a Criterion for the Onset of Instability in Uniformly Rotating Configurations and the Frequency of the Fundamental Mode in Case of Slow Rotation

The theory developed in Paper I is applied to solve two problems in general relativity: to obtain a criterion for the onset of instability in a uniformly rotating configuration via a neutral mode of axisymmetric oscillation; and to obtain an exact and an explicit formula for the square of the frequency of the fundamental axisymmetric mode of oscillation of a configuration rotating uniformly but slowly.