Neutral points of oscillation modes along equilibrium sequences of rapidly rotating polytropes in general relativity: Application of the Cowling approximation

The relativistic Cowling approximation in which all metric perturbations are omitted is applied to nonaxisymmetric infinitesimal oscillations of uniformly rotating general relativistic polytropes. Frequencies of lower order f-modes, which are important in analysis of secular instability driven by gravitational radiation, are investigated, and neutral points of the mode along equilibrium sequences of rotating polytropes are determined. Since this approximation becomes more accurate as stars are more relativistic and/or as they rotate more rapidly, we will be able to analyze how a rotation period of a neutron star may be limited by this instability. Possible errors in determining neutral points caused by omitting metric perturbations are also estimated.