Non-axisymmetric oscillations of rapidly rotating relativistic stars by conformal flatness approximation

TL;DR

This paper introduces a new numerical method using conformal flatness approximation to compute non-axisymmetric oscillation modes of rapidly rotating relativistic stars, enabling analysis of gravitational radiation-driven instabilities.

Contribution

The authors develop and validate a novel numerical code for non-axisymmetric mode calculation in rotating relativistic stars using conformal flatness approximation.

Findings

Good agreement with full theory for low-order modes

Computed sequences of counter-rotating f-modes

Identified modes susceptible to gravitational radiation instability

Abstract

We present a new numerical code to compute non-axisymmetric eigenmodes of rapidly rotating relativistic stars by adopting spatially conformally flat approximation of general relativity. The approximation suppresses the radiative degree of freedom of relativistic gravity and the field equations are cast into a set of elliptic equations. The code is tested against the low-order f- and p-modes of slowly rotating stars for which a good agreement is observed in frequencies computed by our new code and those computed by the full theory. Entire sequences of the low order counter-rotating f-modes are computed, which are susceptible to an instability driven by gravitational radiation.