内容

目次

1 Introduction.- 1.1 Compact Stars.- 1.2 Compact Stars and Relativistic Physics.- 1.3 Compact Stars and Dense-Matter Physics.- 2 General Relativity.- 2.1 Relativity.- 2.2 Lorentz Invariance.- 2.2.1 Lorentz transformations.- 2.2.2 Covariant vectors.- 2.2.3 Energy and momentum.- 2.2.4 Energy-momentum tensor of a perfect fluid.- 2.2.5 Light cone.- 2.3 Scalars, Vectors, and Tensors in Curvilinear Coordinates.- 2.4 Principle of Equivalence of Inertia and Gravitation.- 2.4.1 Photon in a gravitational field.- 2.4.2 Tidal gravity.- 2.4.3 Curvature of spacetime.- 2.4.4 Energy conservation and curvature.- 2.5 Gravity.- 2.5.1 Mathematical definition of local Lorentz frames.- 2.5.2 Geodesics.- 2.5.3 Comparison with Newton’ gravity.- 2.6 Covariance.- 2.6.1 Principle of general covariance.- 2.6.2 Covariant differentiation.- 2.6.3 Geodesic equation from covariance principle.- 2.6.4 Covariant divergence and conserved quantities.- 2.7 Riemann Curvature Tensor.- 2.7.1 Second covariant derivative of scalars and vectors.- 2.7.2 Symmetries of the Riemann tensor.- 2.7.3 Test for flatness.- 2.7.4 Second covariant derivative of tensors.- 2.7.5 Bianchi identities.- 2.7.6 Einstein tensor.- 2.8 Einstein’ Field Equations.- 2.9 Relativistic Stars.- 2.9.1 Metric in static isotropic spacetime.- 2.9.2 The Schwarzschild solution.- 2.9.3 Riemann tensor outside a Schwarzschild star.- 2.9.4 Energy-momentum tensor of matter.- 2.9.5 The Oppenheimer-Volkoff equations.- 2.9.6 Gravitational collapse and limiting mass.- 2.10 Action Principle in Gravity.- 2.10.1 Derivations.- 2.11 Problems for Chapter 2.- 3 Compact Stars: From Dwarfs to Black Holes.- 3.1 Birth and Death of Stars.- 3.2 Objective.- 3.3 Gravitational Units and Neutron Star Size.- 3.3.1 Units.- 3.3.2 Size and number of baryons in a star.- 3.3.3 Gravitational energy of a neutron star.- 3.4 Partial Decoupling of Matter from Gravity.- 3.5 Equations of Relativistic Stellar Structure.- 3.5.1 Interpretation.- 3.5.2 Boundary conditions and stellar sequences.- 3.6 Electrical Neutrality of Stars.- 3.7 “Constancy” of the Chemical Potential.- 3.8 Gravitational Redshift.- 3.8.1 Integrity of an atom in strong fields.- 3.8.2 Redshift in a general static field.- 3.8.3 Comparison of emitted and received light.- 3.8.4 Measurements of M/R from redshift.- 3.9 White Dwarfs and Neutron Stars.- 3.9.1 Overview.- 3.9.2 Fermi-gas equation of state for nucleons and electrons.- 3.9.3 High- and low-density limits.- 3.9.4 Polytropes and Newtonian white dwarfs.- 3.9.5 Nonrelativistic electron region.- 3.9.6 Ultrarelativistic electron region: asymptotic white dwarf mass.- 3.9.7 Nature of limiting mass of dwarfs and neutron stars.- 3.9.8 Degenerate ideal gas neutron star.- 3.10 Improvements in White Dwarf Models.- 3.10.1 Nature of matter at dwarf and neutron star densities.- 3.10.2 Low-density equation of state.- 3.10.3 Carbon and oxygen white dwarfs.- 3.11 Temperature and Neutron Star Surface.- 3.12 Stellar Sequences from White Dwarfs to Neutron Stars.- 3.13 Baryon Number of a Star.- 3.14 Binding Energy of a Neutron Star.- 3.15 Star of Uniform Density.- 3.16 Scaling Solution of the OV Equations.- 3.17 Bound on Maximum Mass of Neutron Stars.- 3.18 Stability.- 3.18.1 Necessary condition for stability.- 3.18.2 Normal modes of vibration: Sufficient condition for stability.- 3.19 Beyond the Maximum-Mass Neutron Star.- 3.20 Black Holes.- 3.20.1 Interior and exterior regions.- 3.20.2 No statics within.- 3.20.3 Black hole densities.- 3.21 Problems for Chapter 3.- 4 Relativistic Nuclear Field Theory.- 4.1 Motivation.- 4.2 Lagrange Formalism.- 4.3 Symmetries and Conservation Laws.- 4.3.1 Internal global symmetries.- 4.3.2 Spacetime symmetries.- 4.4 Boson and Fermion Fields.- 4.4.1 Uncharged and charged scalar fields.- 4.4.2 Uncharged and charged vector fields.- 4.4.3 Dirac fields.- 4.4.4 Neutron and proton.- 4.4.5 Electromagnetic field.- 4.5 Properties of Nuclear Matter.- 4.6 The ? — ? Model.- 4.7 Stationarity of Energy Density.- 4.8 Model with Scalar Self-Interactions.- 4.8.1 Algebraic determination of the coupling constants.- 4.8.2 Symmetric nuclear matter equation of state.- 4.8.3 Negative self-interaction.- 4.9 Introduction of Isospin Force.- 4.10 Inclusion of the Octet of Baryons.- 4.11 High-Density Limit.- 4.12 Effective Versus Renormalized Theory.- 4.13 Bound Versus Unbound Neutron Matter.- 4.13.1 Bound neutron matter.- 4.14 Note on Dimensions.- 4.15 Summary.- 4.16 Problems for Chapter 4.- 5 Neutron Stars.- 5.1 Discovery.- 5.2 Pulsars: The Observational Basis of Neutron Stars.- 5.2.1 Important pulsar discoveries.- 5.2.2 Pulsar periods.- 5.2.3 Individual pulses and pulse profiles.- 5.2.4 Detection biases.- 5.2.5 Two populations of pulsars.- 5.2.6 Supernova associations with pulsars.- 5.2.7 Why pulsars are neutron stars.- 5.2.8 Mass of the Crab pulsar.- 5.2.9 Pulsar masses: observational.- 5.2.10 Pulsar masses: physical bounds.- 5.2.11 Neutron stars: a cosmic coincidence.- 5.2.12 Pulsar ages.- 5.2.13 Evolution of the braking index.- 5.3 Theory of Neutron Stars.- 5.3.1 Nuclear and neutron star matter: Similarities and differences.- 5.3.2 Chemical equilibrium in a star.- 5.3.3 Hadronic composition of neutron stars.- 5.3.4 Superdense matter.- 5.3.5 Neutron star matter.- 5.3.6 Hints for computation.- 5.3.7 Isospin- and charge-favored baryon species.- 5.3.8 Surface of neutron stars.- 5.3.9 Reprise of white dwarfs to neutron stars.- 5.3.10 Development of neutron star sequences.- 5.3.11 Mass as a function of central density.- 5.3.12 Radius—mass characteristic relationship.- 5.3.13 Limiting mass and the equation of state.- 5.4 Constitution of Neutron Stars.- 5.4.1 Beta equilibrium and symmetry energy.- 5.4.2 Hyperon stars.- 5.4.3 Hyperon coupling constants.- 5.4.4 Hyperon populations and the limiting mass.- 5.4.5 Compression modulus and effective nucleon mass.- 5.4.6 Charge neutrality achieved among baryons.- 5.4.7 Pion and kaon condensation.- 5.4.8 Condensation of Free Pions.- 5.5 Tables of Equations of State.- 5.5.1 Low density.- 5.5.2 High density.- 5.6 Problems for Chapter 5.- 6 Rotating Neutron Stars.- 6.1 Motivation.- 6.2 Dragging of Local Inertial Frames.- 6.3 Interior Solution for the Dragging Frequency.- 6.4 Moment of Inertia of a Rotating Relativistic Star.- 6.5 Kepler Angular Velocity in General Relativity.- 6.6 Effect of Frame Dragging on Kepler Frequency.- 6.7 Approximation to the Kepler Frequency.- 6.8 Hartle—Thorne Perturbative Solution.- 6.8.1 Comparison of Perturbative and Numerical Solutions.- 6.9 Imprint of Angular Momentum.- 6.10 Rotating Stars with Realistic Equations of State.- 6.11 Effect of Rotation on Stellar Structure.- 6.12 Gravitational-Wave Instabilities.- 6.13 Problems for Chapter 6.- 7 Limiting Rotational Period and Radius of Neutron Stars.- 7.1 Motivation.- 7.2 The Minimal Constraints.- 7.3 Variational Ansatz.- 7.4 Limiting Value of Rotational Period as a Function of Mass.- 7.5 Test of Sensitivity of Results.- 7.6 General Relativistic Limit on Rotation.- 7.7 Lower Limit on Neutron Star Radius.- 7.8 Discussion and Alternatives.- 7.9 Self-Bound Stars.- 7.10 Summary.- 8 Quark Stars.- 8.1 Introduction.- 8.2 Model of Quark Confinement.- 8.3 Quark Matter Equation of State.- 8.3.1 Zero temperature.- 8.3.2 Massless quark approximation.- 8.3.3 First order in ?s.- 8.4 Quark Star Matter.- 8.5 Strange and Charm Stars.- 8.5.1 General considerations.- 8.5.2 Strange quark matter.- 8.5.3 Stability considerations.- 8.6 Problems for Chapter 8.- 9 Hybrid Stars.- 9.1 Introduction.- 9.2 Constant-Pressure Phase Transition.- 9.2.1 Purely neutron star.- 9.2.2 Enforced local charge neutrality.- 9.3 The Confined—Deconfined Phase Transition in Neutron Stars.- 9.3.1 Conservation laws are global—not local.- 9.3.2 Degrees of freedom in a multicomponent substance.- 9.3.3 Nuclear symmetry energy and a coulomb lattice.- 9.3.4 Phase diagram.- 9.3.5 Two energy scales.- 9.4 Large-Scale Structure of a Hybrid Star.- 9.4.1 Energy budget in the reapportionment of charge.- 9.5 Crystalline Structure of the Mixed Phase.- 9.5.1 Crystalline structure as a function of stellar mass.- 9.5.2 Possible implications for glitches.- 9.6 Tables of Equation of State for Hybrid Stars.- 9.7 Problems for Chapter 9.- 10 Bose Condensates in Neutron Stars.- 10.1 Relativistic Mean—Field Model with Kaons.- 10.2 Equation of State with a Kaon Condensate.- 10.2.1 Maxwell versus Gibbs.- 10.2.2 Dependence on parameters.- 10.2.3 Particle populations.- 10.2.4 Comment on coupling schemes.- 10.2.5 Comment on hyperons.- 10.2.6 Mixed-phase properties.- 10.3 Stellar Properties.- 10.3.1 Large-scale features.- 10.3.2 Geometrical structure in the mixed phase.- 10.3.3 Pulsar glitches.- 10.4 Summary.- 10.5 Problems for Chapter 10.- 11 Consequences and Signals of Phase Transitions.- 11.1 Introduction.- 11.2 Mechanism for Formation of Low-Mass Black Holes.- 11.2.1 Hyperonization-induced collapse.- 11.2.2 Deconfinement-induced collapse.- 11.2.3 Density profiles.- 11.2.4 Discussion.- 11.3 A Third Class of Stable Compact Stars.- 11.3.1 Introduction.- 11.3.2 Stability of nonidentical twins.- 11.3.3 Cause of stability of a third class of stars.- 11.3.4 Detection and formation mechanisms.- 11.3.5 Conclusions and prospects.- 11.4 Phase Transition Signal in Pulsar Timing.- 11.4.1 Evolutionary path of neutron stars.- 11.4.2 Calculation.- 11.4.3 Spin-up era.- 11.4.4 X-ray pulsars in low-mass binaries.- 11.5 Caveats.- 12 Strange Stars.- 12.1 The Strange Matter Hypothesis.- 12.2 Compatibility of the Hypothesis with Present Knowledge.- 12.2.1 Energetic considerations.- 12.2.2 The universe and its evolution.- 12.2.3 Stability of nuclei against decay to strange matter.- 12.2.4 Stability of nuclei to conversion by strange nuggets.- 12.2.5 Terrestrial searches.- 12.2.6 Summary, prospects, and challenges.- 12.3 Submillisecond Pulsars.- 12.3.1 The fine-tuning problem.- 12.3.2 Limits to neutron star rotation.- 12.3.3 Implausibly high central densities.- 12.3.4 Strange stars as fast rotors.- 12.3.5 Out of the impasse.- 12.3.6 Motivation for searches and prospects for discovery.- 12.4 Structure of Strange Stars.- 12.5 Simultaneous Existence of Strange and Neutron Stars.- 12.6 Strange Stars to Strange Dwarfs.- 12.6.1 Strange stars with nuclear crusts.- 12.6.2 Nuclear crust and pulsar glitches.- 12.6.3 Strange dwarfs with nuclear crusts.- 12.6.4 Stability.- 12.6.5 Possible new class of dense white dwarfs.- 12.7 Conclusion.- Useful Astronomical Data.- Books for Further Study.- References.