ON THE OSCILLATION SPECTRA OF ULTRACOMPACT STARS - AN EXTENSIVE SURVEY OF GRAVITATIONAL-WAVE MODES

An extensive survey of gravitational-wave modes for uniform density st ars is presented. The study covers stars ranging in compactness from R /M = 100 to the limit of stability in general relativity: R/M = 9/4. W e establish that polar and axial gravitational-wave modes exist for al l these stellar models. Moreover, there are two distinct families of b oth axial and polar modes. We discuss the physics of these modes and a rgue that one family is primarily associated with the interior of the star, while the second family is mainly associated with the stellar su rface. We also show that the problem of axial perturbations has all th e essential features of the polar problem as far as gravitational wave s are concerned. This means that the axial problem is much more import ant than has previously been assumed. We also find some surprising fea tures, such as avoided crossings between the polar gravitational-wave modes and the Kelvin-f-mode as the star becomes very compact. This see ms to suggest that the f-mode should be considered on equal footing wi th the polar w-modes for ultracompact stars. All modes may have the ma in character of trapped modes inside the curvature potential barrier f or R/M < 3.