Axial Instability of Rotating Relativistic Stars

Perturbations of rotating relativistic stars can be classified by theirbehavior under parity. For axial perturbations (r-modes), initial data withnegative canonical energy is found with angular dependence $e^{im\phi}$ for allvalues of $m\geq 2$ and for arbitrarily slow rotation. This implies instability(or marginal stability) of such perturbations for rotating perfect fluids. Thislow $m$-instability is strikingly different from the instability to polarperturbations, which sets in first for large values of $m$. The timescale forthe axial instability appears, for small angular velocity $\Omega$, to beproportional to a high power of $\Omega$. As in the case of polar modes,viscosity will again presumably enforce stability except for hot, rapidlyrotating neutron stars. This work complements Andersson's numericalinvestigation of axial modes in slowly rotating stars.Comment: Latex, 18 pages. Equations 84 and 85 are corrected. Discussion of timescales is corrected and update