Results on the spectrum of R-Modes of slowly rotating relativistic stars

TL;DR

This paper analyzes the spectrum of axial perturbations in slowly rotating relativistic stars, revealing instabilities, the presence of a continuous spectrum, and the impact of higher-order rotational corrections on stability.

Contribution

It provides a detailed spectral analysis of axial perturbations in relativistic stars, highlighting instabilities and the significance of higher-order rotational effects.

Findings

Identified instability due to a continuum of non-real eigenvalues.

Discovered a special structure in the resolvent affecting the spectrum.

Higher order rotational corrections can alter the star's stability.

Abstract

The paper considers the spectrum of axial perturbations of slowly uniformly rotating general relativistic stars in the framework of Y. Kojima. In a first step towards a full analysis only the evolution equations are treated but not the constraint. Then it is found that the system is unstable due to a continuum of non real eigenvalues. In addition the resolvent of the associated generator of time evolution is found to have a special structure which was discussed in a previous paper. From this structure it follows the occurrence of a continuous part in the spectrum of oscillations at least if the system is restricted to a finite space as is done in most numerical investigations. Finally, it can be seen that higher order corrections in the rotation frequency can qualitatively influence the spectrum of the oscillations. As a consequence different descriptions of the star which are equivalent to first order could lead to different results with respect to the stability of the star.