NONAXISYMMETRIC NEUTRAL-MODES IN ROTATING RELATIVISTIC STARS

We study nonaxisymmetric perturbations of rotating relativistic stars modeled as perfect-fluid equilibria. Instability to a mode with angula r dependence exp (im phi) sets in when the frequency of the mode vanis hes. The locations of these zero-frequency modes along sequences of ro tating stars are computed for the first time in the framework of gener al relativity. We consider models of uniformly rotating stars with pol ytropic equations of state, finding that the relativistic models are u nstable to nonaxisymmetric modes at significantly smaller values of ro tation than in the Newtonian limit. Most strikingly, the m = 2 bar mod e can become unstable even for soft polytropes of index N less than or equal to 1.3, while in Newtonian theory it becomes unstable only for stiff polytropes of index N less than or equal to 0.808. If rapidly ro tating neutron stars are formed by the accretion-induced collapse of w hite dwarfs, instability associated with these nonaxisymmetric, gravit ational-wave driven modes may set an upper limit on neutron-star rotat ion. Consideration is restricted to perturbations that correspond to p olar perturbations of a spherical star. A study of axial perturbations is in progress.