## Rotating Relativistic StarsThe masses of neutron stars are limited by an instability to gravitational collapse, and an instability driven by gravitational waves limits their spin. Their oscillations are relevant to x-ray observations of accreting binaries and to gravitational wave observations of neutron stars formed during the coalescence of double neutron-star systems. This volume pulls together over 40 years of research to provide graduate students and researchers in astrophysics, gravitational physics, and astronomy with the first self-contained treatment of the structure, stability and oscillations of rotating neutron stars. This monograph treats the equations of stellar equilibrium; key approximations, including slow rotation and perturbations of spherical and rotating stars; stability theory and its applications, from convective stability to the r-mode instability; and numerical methods for computing equilibrium configurations and the nonlinear evolution of their oscillations. The presentation of fundamental equations, results, and applications is accessible to readers who do not need the detailed derivations. |

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### Contents

3+1 split action Lagrangian and Hamiltonian formalisms | 31 |

Asymptotics virial identities and nonaxisymmetric | 59 |

Numerical schemes | 98 |

Equilibrium models | 109 |

Approximation methods for equilibria | 135 |

Perturbation theory of relativistic ﬂuids | 157 |

Quasinormal modes | 206 |

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### Common terms and phrases

accreting ADM mass amplitude angular momentum angular velocity Astron Astrophys asymptotic axial axisymmetric barotropic baryon binary black hole canonical energy collapse components conﬁguration conservation constant constraint coordinates Cowling approximation deﬁned deﬁnition differentially rotating dynamical Einstein-Euler energy density entropy EOSs equilibrium Euler equation evolution ﬁeld equation ﬁnd ﬁxed ﬂat ﬂow ﬂuid ﬂuid element frequency function gauge gravitational radiation gravitational waves hyperons hypersurface implies inertial inﬁnity instability integral Killing vector Lagrangian Lie derivative linear magnetic ﬁeld mass-shedding limit maximum mass metric modes multipole multipole moments neutron stars Newtonian nonaxisymmetric nonlinear nonrotating normal numerical obtained oscillations parameter perturbed Phys polar polytropes pulsations quadrupole r-mode rapidly rotating rotating neutron stars rotating relativistic stars rotating stars rotation rate satisﬁes scalar sequence simulations solution spacetime spatial speciﬁc spherical star stability stationary strange quark stress-energy tensor surface symmetry tensor theorem timescale uniformly rotating vanishes vector ﬁeld viscosity