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Abstract

The problem of relativistic stellar pulsations is studied in a somewhat ad hoc approximation that ignores all fluid motions. This Inverse Cowling Approximation (ICA) is motivated by two observations. (1) For highly damped (w-mode) oscillations the fluid plays very little role. (2) If the fluid motion is neglected, the problem for polar oscillations modes becomes similar to that for axial modes. Using the ICA, we find a polar mode spectrum that has all features of the w-mode spectrum of the full problem. Moreover, in the limit of superdense stars, we find the ICA spectrum to be qualitatively similar to that of the axial modes. These results clearly show the importance of general relativity for the pulsation modes of compact stars, and that there are modes whose existence does not depend on motions of the fluid at all, namely pure `space-time' modes.