Slowly rotating relativistic stars. VI - Stability of the quasi-radial modes.
Dynamical analysis of the quasi-radial modes of slowly and rigidly rotating, relativistic stars. The quasi-radial modes are those modes which would be radial if the star were not rotating. They are the crucial modes for determining the stability of the rotating star and also the modes which store energy for the longest time against dissipation by gravitational radiation. An equation is derived that makes it possible to calculate the effects of the slow and rigid star rotation on the frequency of the quasi-radial modes of oscillation of relativistic stars. The rotation is treated to second order in the angular velocity, but no other approximations are made.