Post-Newtonian frequencies for the pulsations of rapidly rotating neutron stars

The present study reviews and extends the formalism for computing the oscillation frequencies of rapidly rotating stars in the post-Newtonian approximation. The appropriate boundary conditions to be imposed on the post-Newtonian mode solutions and their role in determining the post-Newtonian correction to the mode eigenfrequency are discussed. Numerical results for the post-Newtonian oscillation frequencies are presented. The accuracy of this method is estimated by comparing the post-Newtonian frequencies for nonrotating stars with the full, general-relativistic mode frequencies. The post-Newtonian results are found to agree with the exact ones to within a few percent for typical neutron stars. The frequency corrections for the l = m f-modes of rotating stars are computed, and, in the post-Newtonian approximation, the critical angular velocities where these frequencies vanish are determined.

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