Accuracy of the relativistic Cowling approximation in slowly rotating stars

TL;DR

This study evaluates the accuracy of the relativistic Cowling approximation in modeling oscillation frequencies of slowly rotating stars, finding it to be within 20% of full general relativity calculations, especially for higher-order modes.

Contribution

It provides a quantitative assessment of the Cowling approximation's accuracy in relativistic stars, highlighting its reliability for certain oscillation modes.

Findings

Approximation differs by less than 20% from full GR results.

Higher-order modes are modeled more accurately.

The approximation remains useful for typical relativistic stellar models.

Abstract

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.