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Axial oscillations relevant to the r-mode instability are studied with slowrotation formalism in general relativity. The approximate equation governingthe oscillations is derived with second-order rotational corrections. Theequation contains an effective 'viscosity-like' term, which originates fromcoupling to the polar g-mode displacements. The term plays a crucial role onthe resonance point, where the disturbance on the rotating stars satisfies acertain condition at the lowest order equation. The effect is significant fornewly born hot neutron stars, which are expected to be subject to thegravitational radiation driven instability of the r-mode.Comment: 13pages, no figures, accepted for publication in Physical Review

Approximate equation relevant to axial oscillations on slowly rotating relativistic stars