Accuracy of the relativistic Cowling approximation in slowly rotating stars

We have calculated the non-radial oscillation in slowly rotating relativistic stars with the Cowling approximation. The frequencies are compared with those based on the complete linearized equations of general relativity. It is found that the results with the approximation differ by less than about $20 %$ for typical relativistic stellar models. The approximation is more accurate for higher-order modes as in the Newtonian case.