G-modes of non-radially pulsating relativistic stars - The slow-motion formalism

A new formalism, designed explicitly for the numerical study of g-modes of nonrotating, perfect-fluid, relativistic stars, is presented. The formalism is based on the analysis of Thorne and Campolattaro (1967), but with the following changes: (1) a choice of perturbation variables more suited to the numerical analysis of the low-frequency g-mode pulsations, (2) the introduction of an instantaneous-gravity approximation that replaces the boundary condition of outgoing gravitational radiation at infinity by a nonradiative, Newtonian-like boundary condition, and (3) an energy principle for determining the damping time of a mode due to gravitational radiation. The new formalism is applied to the study of g-mode pulsations of neutron star models with a polytropic equation of state.