Abstract
The determination of the eigenvalues and eigenfunctions of the differential equations governing the non-radial oscillations of a heterogeneous compressible sphere, presents a complex mathematical problem. In previous discussions, the perturbation of the gravitational potential has always been neglected to simplify the problem. Even so only a few approximate solutions are known and for rather artificial models. We plan to compute by numerical integrations the exact eigenvalues and their solutions for some actual models of massive stars and use them to discuss the vibrational stability of the models and the effects of superadiabatic gradients on dynamical stability towards non-radial perturbations. In this paper, the results are given for the second spherical harmonic for one of the models.
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