Normal modes of relativistic systems in post-Newtonian approximation and the stability curve of r-modes

Abstract

In part I, we use the post-Newtonian (pn) order of Liouville's equation to study the normal modes of oscillation of a spherically symmetric relativistic system. Perturbations that are neutral in Newtonian approximation develop into a new sequence of normal modes. In part II, stability curve of r-modes of neutron stars are calculated by considering vorticity-shear viscosity coupling. As an application, the loss of angular momentum through gravitational radiation, driven by the excitation of r-modes, is considered in neutron stars having rotation frequencies smaller than the associated critical frequency.