Ther‐Mode Oscillations in Relativistic Rotating Stars

The axial mode oscillations are examined for relativistic rotating stars withuniform angular velocity. Using the slow rotation formalism and the Cowlingapproximation, we have derived the equations governing the r-mode oscillationsup to the second order with respect to the rotation. In the lowest order, theallowed range of the frequencies is determined, but corresponding spatialfunction is arbitrary. The spatial function can be decomposed in non-barotropicregion by a set of functions associated with the differential equation of thesecond-order corrections. The equation however becomes singular in barotropicregion, and a single function can be selected to describe the spatialperturbation of the lowest order. The frame dragging effect among therelativistic effects may be significant, as it results in rather broad spectrumof the r-mode frequency unlike in the Newtonian first-order calculation.Comment: 19 pages, 4 figures, AAS LaTeX, Accepted for publication in The Astrophysical Journa