The relativistic theory of non-radial oscillations of stars is based on the study of the scattering of gravitational waves by the potential barrier generated by the spacetime curvature. The corresponding newtonian theory is based on the solution of an eigenvalue problem associated to the relevant equations that couple the perturbations of the gravitational field with the perturbations of the fluid. In this paper we show that although the relativistic theory uses a completely different physical approach, when applied to newtonian stars in its exact form it reproduces all the results of the newtonian theory. We show that the g, f, p-modes, that according to Cowling's classification are originated by the restoring force that is prevailing in the perturbed fluid, are also coded in the gravitational field. We discuss the reason why the characteristic damping time associated with the emission of gravitational waves is difficult to determine.