Space-time modes of relativistic stars

The problem of relativistic stellar pulsations is studied in a somewhat adhoc approximation that ignores all fluid motions. This {\em Inverse CowlingApproximation} (ICA) is motivated by two observations: 1) For highly damped($w$-mode) oscillations the fluid plays very little role. 2) If the fluidmotion is neglected the problem for polar oscillation modes becomes similar tothat for axial modes. Using the ICA we find a polar mode spectrum that has allfeatures of the $w$-mode spectrum of the full problem. Moreover, in the limitof superdense stars, we find the ICA spectrum to be qualitatively similar tothat of the axial modes. These results clearly show the importance of generalrelativity for the pulsation modes of compact stars, and that there are modeswhose existence do not depend on motions of the fluid at all; pure``spacetime'' modes.Comment: 4 pages, MN.STY, 2 postscript figure