Accuracy of relativistic Cowling approximation in protoneutron star asteroseismology

Understand

The relativistic Cowling approximation, where the metric perturbations are neglected during the fluid oscillations, is often adopted for considering the gravitational waves from the protoneutron stars (PNSs) provided via core-collapse supernova explosions.

• In this study, we evaluate how the Cowling approximation works well by comparing the frequencies with the Cowling approximation to those without the approximation.
• Then, we find that the behavior of the frequencies with the approximation is qualitatively the same way as that without the approximation, where the frequencies with the approximation can totally be determined within $\sim 20\%$ accuracy.
• In particular, the fundamental mode with the Cowling approximation is overestimated.