A new approach to the study of quasi-normal modes of rotating stars

TL;DR

This paper introduces a spectral method to compute quasi-normal modes of rotating relativistic stars by expanding perturbations in circular harmonics and applying generalized boundary conditions, demonstrated on slowly rotating stars.

Contribution

It presents a novel spectral approach for analyzing oscillations of rotating stars, extending techniques from non-rotating cases to include rotation effects.

Findings

Successfully computed quasi-normal mode frequencies for slowly rotating stars.

Validated the method against known results for non-rotating stars.

Provides a framework for studying more rapidly rotating stellar models.

Abstract

We propose a new method to study the quasi-normal modes of rotating relativistic stars. Oscillations are treated as perturbations in the frequency domain of the stationary, axisymmetric background describing a rotating star. The perturbed quantities are expanded in circular harmonics, and the resulting 2D-equations they satisfy are integrated using spectral methods in the (r,theta)-plane. The asymptotic conditions at infinity, needed to find the mode frequencies, are implemented by generalizing the standing wave boundary condition commonly used in the non rotating case. As a test, the method is applied to find the quasi-normal mode frequencies of a slowly rotating star.