Relativistic R-modes in slowly rotating neutron stars

We investigate the properties of relativistic r-modes of slowly rotating neutron stars by using a relativistic version of the Cowling approximation. In our formalism, we take into account the influence of the Coriolis-like force on the stellar oscillations, but ignore the effects of the centrifugal-like force. For three neutron star models, we calculated the fundamental r-modes with l' = m = 2. We find that the oscillation frequency (sigma) over bar of the fundamental r-mode is given in a good approximation by (sigma) over bar approximate to kappa(0)Omega, where (sigma) over bar is defined in the corotating frame at spatial infinity and Omega is the angular frequency of rotation of the star. The proportional coefficient no is only weakly dependent on Q, but it strongly depends on the relativistic parameter GM/c(2)R, where M and R are the mass and the radius of the star. All the fundamental r-modes with V = m computed in this study are discrete modes with distinct regular eigenfunctions.