We study nonaxisymmetric perturbations of rotating relativistic stars.
modeled as perfect-fluid equilibria. Instability to a mode with angular
dependence exp(imϕ) sets in when the frequency of the mode vanishes. The
locations of these zero-frequency modes along sequences of rotating stars are
computed in the framework of general relativity. We consider models of
uniformly rotating stars with polytropic equations of state, finding that the
relativistic models are unstable to nonaxisymmetric modes at significantly
smaller values of rotation than in the Newtonian limit. Most strikingly, the
m=2 bar mode can become unstable even for soft polytropes of index N≤1.3, while in Newtonian theory it becomes unstable only for stiff polytropes
of index N≤0.808. If rapidly rotating neutron stars are formed by the
accretion-induced collapse of white dwarfs, instability associated with these
nonaxisymmetric, gravitational-wave driven modes may set an upper limit on
neutron-star rotation. Consideration is restricted to perturbations that
correspond to polar perturbations of a spherical star. A study of axial
perturbations is in progress.Comment: 57 pages, 9 figure