Torsional oscillations of slowly rotating relativistic stars

We study the effects of rotation on the torsional modes of oscillating relativistic stars with a solid crust. Earlier works in Newtonian theory provided estimates of the rotational corrections for the torsional modes and suggested that they should become Chandrasekhar-Friedman-Schutz unstable, even for quite low rotation rates. In this work, we study the effect of rotation in the context of general relativity using elasticity theory and in the slow-rotation approximation. We find that the Newtonian picture does not change considerably. The inclusion of relativistic effects leads only to quantitative corrections. The degeneracy of modes for different values of m is removed, and modes with = m are shifted towards zero frequencies and become secularly unstable at stellar rotational frequencies 20-30 Hz.

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