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We propose a new method to study the quasi-normal modes of rotatingrelativistic stars. Oscillations are treated as perturbations in the frequencydomain of the stationary, axisymmetric background describing a rotating star.The perturbed quantities are expanded in circular harmonics, and the resulting2D-equations they satisfy are integrated using spectral methods in the(r,theta)-plane. The asymptotic conditions at infinity, needed to find the modefrequencies, are implemented by generalizing the standing wave boundarycondition commonly used in the non rotating case. As a test, the method isapplied to find the quasi-normal mode frequencies of a slowly rotating star.

A new approach to the study of quasi-normal modes of rotating stars