The rotational modes of relativistic stars: Numerical results

TL;DR

This paper investigates the inertial modes of slowly rotating relativistic stars using numerical methods, focusing on their stability and gravitational wave emission, and finds relativistic effects slightly stabilize these modes without altering previous instability conclusions.

Contribution

It provides numerical analysis of inertial modes in relativistic stars, extending prior Newtonian studies and assessing relativistic stabilization effects on gravitational-wave-driven instabilities.

Findings

Inertial modes are hybrid axial-polar in relativistic stars.

Relativistic effects slightly stabilize inertial modes.

Unstable r-modes remain largely unaffected by relativistic corrections.

Abstract

We study the inertial modes of slowly rotating, fully relativistic compact stars. The equations that govern perturbations of both barotropic and non-barotropic models are discussed, but we present numerical results only for the barotropic case. For barotropic stars all inertial modes are a hybrid mixture of axial and polar perturbations. We use a spectral method to solve for such modes of various polytropic models. Our main attention is on modes that can be driven unstable by the emission of gravitational waves. Hence, we calculate the gravitational-wave growth timescale for these unstable modes and compare the results to previous estimates obtained in Newtonian gravity (i.e. using post-Newtonian radiation formulas). We find that the inertial modes are slightly stabilized by relativistic effects, but that previous conclusions concerning eg. the unstable r-modes remain essentially unaltered when the problem is studied in full general relativity.