Non-axisymmetric oscillations of differentially rotating relativistic stars

Non-axisymmetric oscillations of differentially rotating stars are studied using both slow rotation and Cowling approximation. The equilibrium stellar models are relativistic polytropes where differential rotation is described by the relativistic j-constant rotation law. The oscillation spectrum is studied versus three main parameters: the stellar compactness $M\mathrm{/}R$, the degree of differential rotation $A$ and the number of maximun couplings ${\mathrm{\ell }}_{\mathrm{m}\mathrm{a}\mathrm{x}}$. It is shown that the rotational splitting of the non-axisymmetric modes is strongly enhached by increasing the compactness of the star and the degree of differential rotation. Finally, we investigate the relation between the fundamental quadrupole mode and the corotation band of differentially rotating stars.