Slowly rotating relativistic stars. IIIA. The static stability criterion recovered.

The static stability criterion for slowly rotating relativistic stars of Hartle and Thorne is corrected to properly compute the shape of the neutral mode of oscillation of a marginally stable rotating star to zeroth order in the rotation. The correction consists in taking into account the rotation-induced mixing between the neutral radial mode and neutral convective modes. The resulting criterion gives a simple method of analyzing the effect of a slow and rigid rotation on the stability of an isentropic stellar model. Like the static stability criterion for nonrotating stars, the method does not involve solving the full dynamical equations for the pulsations of the rotating star. Instead, it involves constructing a family of equilibrium configurations with a specified differential rotation and then comparing the masses of these configurations with the masses of the uniformly rotating models.