Results on the spectrum of r-modes of slowly rotating, relativistic stars

Abstract

The paper considers the spectrum of axial perturbations (‘pure r-modes’) of slowly uniformly rotating, general relativistic stars. In a first step towards a full analysis, we analyse the evolution equations without the constraint. It is found that the system is unstable due to a continuum of oscillation frequencies with real parts smaller than zero. In addition, the resolvent of the corresponding generator of time evolution is found to have a special structure which was considered in a previous investigation on the oscillations of spherical Newtonian stars. From this structure follows the occurrence of a continuous part in the oscillation spectrum if the system is artificially restricted to a finite space, as is the case in most numerical investigations. Up to first order in the angular velocity Ω of the star that continuous part coincides with a corresponding part found in the low-frequency approximation.