Introduction

Neutron stars more than a few minutes old are uniformly rotating and satisfy to high accuracy the equation of state that describes cold neutron-star matter. As described in Chapter 5, their 2-dimensional family of equilibria is bounded by four curves: at low central density by a sequence of marginally stable configurations having minimum mass at constant angular momentum; at high density by a sequence of marginally stable configurations having maximum mass at constant angular momentum; by the sequence of nonrotating stars; and by the sequence of stars rotating at the Kepler (mass-shedding) limit on angular velocity. A nonaxisym-metric instability driven by gravitational radiation (the CFS instability) is likely to set an upper limit on rotation more stringent than the Kepler limit, drawing a more restrictive boundary at large rotation on the surface of stable equilibria.

Finding these bounding lines of marginal stability is a primary focus of work on the stability theory of relativistic stars. This chapter is devoted to a detailed presentation of this theory and several of its principal results. The presentation here is restricted to linear stability theory, to finding criteria for stability of first-order perturbations of an equilibrium. Numerical treatments of the nonlinear evolution of stable and unstable modes are discussed in Chapter 10.