Stability of relativistic stars

Stable relativistic stars form a two-parameter family, parametrized by mass and angular velocity. Limits on each of these quantities are associated with relativistic instabilities discovered by Chandrasekhar: A radial instability, to gravitational collapse or explosion, marks the upper and lower limits on their mass; and an instability driven by gravitational waves may set an upper limit on their spin. Our summary of relativistic stability theory given here is based on and includes excerpts from the book Rotating Relativistic Stars, by the present authors (Friedman & Sterigioulas 2011).