Quasi-toroidal oscillations in rotating relativistic stars

Abstract

Quasi-toroidal oscillations in slowly rotating stars are examined in the framework of general relativity. The oscillation frequency to first order of the rotation rate is not a single value even for uniform rotation unlike the Newtonian case. All the oscillation frequencies of the r-modes are purely neutral and form a continuous spectrum limited to a certain range. The allowed frequencies are determined by the resonance condition between the perturbation and background mean flow. The resonant frequency varies with the radius according to general relativistic dragging effect.