A NEW NUMERICAL APPROACH TO THE OSCILLATION MODES OF RELATIVISTIC STARS

The oscillation modes of a simple polytropic stellar model are studied . Using a new numerical approach (based on integration for complex coo rdinates) to the problem for the stellar exterior we have computed the eigenfrequencies of the highly damped w modes. The results obtained a gree well with recent ones of Leins, Nollert & Soffel. Specifically, w e are able to explain why several modes in this regime of the complex frequency plane could not be identified within the WKB approach of Kok kotas & Schutz. Furthermore, we have established that the 'kink' that was a prominent feature of the spectra of Kokkotas & Schutz, but which did not appear in the results of Leins et al., was a numerical artefa ct. Using our new numerical code we are also able to compute, for the first time, several of the slowly damped (p) modes for the considered stellar models. For very compact stars we find, somewhat surprisingly, that the damping of these modes does not decrease monotonically as on e proceeds to higher oscillation frequencies. The existence of low-ord er modes that damp away much faster than anticipated may have implicat ions for questions regarding stellar stability and the lifetime of gra vitational-wave sources. The present results illustrate the accuracy a nd reliability of the complex-coordinate method and indicate that the method could prove to be of great use also in problems involving rotat ing stars. There is no apparent reason why the complex-coordinate appr oach should not extend to rotating stars, whereas it is accepted that all previous methods will fail to do so.