Axial instability of rotating relativistic stars

Abstract

Perturbations of rotating relativistic stars can be classified by their behavior under parity. For axial perturbations (r-modes), initial data with negative canonical energy is found with angular dependence $e^{im\varphi }$ for all values of $m\ge 2$ and for arbitrarily slow rotation. This implies instability (or marginal stability) of such perturbations for rotating perfect fluids. This low $m$-instability is strikingly different from the instability to polar perturbations, which sets in first for large values of $m$. The timescale for the axial instability appears, for small angular velocity $\Omega$, to be proportional to a high power of $\Omega$. As in the case of polar modes, viscosity will again presumably enforce stability except for hot, rapidly rotating neutron stars. This work complements Andersson's numerical investigation of axial modes in slowly rotating stars.

Latex, 18 pages. Equations 84 and 85 are corrected. Discussion of timescales is corrected and updated

References in corpus (4)

• A new class of unstable modes of rotating relativistic stars
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• Nonaxisymmetric Neutral Modes in Rotating Relativistic Stars
• Neutral Points of Oscillation Modes along Equilibrium Sequences of Rapidly Rotating Polytropes in General Relativity --- Application of The Cowling Approximation ---

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