Approximate equation relevant to axial oscillations on slowly rotating relativistic stars

TL;DR

This paper derives an approximate equation for axial oscillations in slowly rotating relativistic stars, highlighting a viscosity-like term affecting resonance and instability in hot neutron stars.

Contribution

It introduces a second-order rotational correction to the oscillation equation, revealing a coupling effect crucial for understanding r-mode instability.

Findings

Effective viscosity-like term influences resonance conditions.

Coupling to polar g-modes affects oscillation behavior.

Implications for gravitational wave emission from neutron stars.

Abstract

Axial oscillations relevant to the r-mode instability are studied with slow rotation formalism in general relativity. The approximate equation governing the oscillations is derived with second-order rotational corrections. The equation contains an effective 'viscosity-like' term, which originates from coupling to the polar g-mode displacements. The term plays a crucial role on the resonance point, where the disturbance on the rotating stars satisfies a certain condition at the lowest order equation. The effect is significant for newly born hot neutron stars, which are expected to be subject to the gravitational radiation driven instability of the r-mode.