Rotating Relativistic Stars.

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Preface; List of symbols; Conventions, notation, and mathematical preliminaries; Units, metric and physical constants; Derivatives and integrals; Asymptotic notation: O and o; 1 Stationary, axisymmetric equilibria; 1.1 Perfect fluids; 1.2 The spacetime of a rotating star; 1.3 Einstein's field equation; 1.4 Hydrostationary equilibrium equation; 1.5 The Poincare-Wavre theorem; 1.6 Equation of state; 1.7 Rotation law; 1.8 Equilibrium quantities; 2 3+1 split, action, Lagrangian, and Hamiltonian formalisms; 2.1 The 3+1 split; 2.2 Action for perfect-fluid spacetimes.

2.2.1 Summary of results2.2.2 Lagrangian formalism and Lagrangian displacements; 2.2.3 Gravitational action; 2.2.4 Action for the Einstein-Euler system; 2.2.5 Hamiltonian formalism; 2.3 Gauge freedom and trivial displacements; 2.4 Symmetry under trivial displacements implies conservation of circulation; 3 Asymptotics, virial identities, and nonaxisymmetric equilibria; 3.1 ADM mass and angular momentum; 3.2 Asymptotic behavior of equilibria; 3.2.1 Asymptotic behavior of the metric; 3.3 Virial identities; 3.3.1 Virial relation for stationary spacetimes.

3.3.2 Virial theorem associated with a pseudotensor3.3.3 2D virial identity; 3.4 ADM mass = Komar mass; 3.5 First law of thermodynamics for relativistic stars; 3.6 Nonaxisymmetric equilibria; 3.6.1 Dedekind-like configurations; 3.6.2 Jacobi-like configurations and helical symmetry; 4 Numerical schemes; 4.1 The KEH scheme; 4.1.1 Field equation; 4.1.2 Integral representation; 4.1.3 Iterative procedure; 4.1.4 The CST compactification; 4.1.5 Numerical issues; 4.2 Butterworth and Ipser (BI); 4.3 Bonazzola et al. and Lorene/rotstar; 4.4 Ansorg et al. (AKM); 4.5 Direct comparison of numerical codes.

5 Equilibrium models5.1 Models in uniform rotation; 5.1.1 Bulk properties; 5.1.2 Sequences of equilibrium models; 5.1.3 Empirical relations for the mass-shedding limit; 5.1.4 Upper limits on mass and rotation: Theory versus observation; 5.1.5 Maximum mass set by causality; 5.1.6 Minimum period set by causality; 5.1.7 Moment of inertia and ellipticity; 5.1.8 Rotating strange quark stars; 5.2 Proto -- neutron-star models; 5.3 Magnetized equilibrium models; 6 Approximation methods for equilibria; 6.1 Slow-rotation approximation; 6.1.1 The nonrotating limit.

6.1.2 Stationary axisymmetric spacetime in quasi-Schwarzschild coordinates6.1.3 Slow-rotation expansion to O(); 6.1.4 Slow-rotation expansion to O(2); 6.1.5 Physical properties in the slow-rotation approximation; 6.2 Spatial conformal flatness and quasiequilibrium approximations; 6.2.1 Spatial conformal flatness: The IWM-CFC approximation; 6.2.2 Irrotational flow and helical symmetry; 6.2.3 Waveless formulation for binary systems: Beyond conformal flatness; 6.3 Exact vacuum solutions; 6.3.1 The 3-parameter Manko et al. solution; 6.3.2 Other exact vacuum solutions.

7 Perturbation theory of relativistic fluids.

This volume provides the first self-contained treatment of the structure, stability and oscillations of rotating neutron stars.

Includes bibliographical references and index.

English.

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