Secular instability of rotating Newtonian stars

The effect of gravitational radiation and of viscosity on the stability of rotating self-gravitating fluids is analyzed. It is found that all rotating stars are unstable or marginally unstable to gravitational radiation. The stability criterion for stability against viscosity is shown to involve the canonical energy in a rotating frame, a functional invariant under gauge transformations associated with the trivial displacements. A star is locally stable against viscosity if and only if the specific entropy increases outward (in the sense of decreasing pressure). The behavior of normal modes is considered and applied to elucidate the generic radiation-induced instability.