Axial instability of rotating relativistic stars

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 phi) for all values of m greater than or equal to 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.