Compact Stars

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 Lorentz Invariance.- 2.1.1 Lorentz transformations.- 2.1.2 Covariant vectors.- 2.1.3 Energy-momentum tensor of a perfect fluid.- 2.1.4 Light cone.- 2.2 Scalars, Vectors, and Tensors in Curvilinear Coordinates.- 2.3 Principle of Equivalence of Inertia and Gravitation.- 2.3.1 Photon in a gravitational field.- 2.3.2 Tidal gravity.- 2.3.3 Curvature of spacetime.- 2.3.4 Energy conservation and curvature.- 2.4 Gravity.- 2.4.1 Mathematical definition of local Lorentz frames.- 2.4.2 Geodesics.- 2.4.3 Comparison with Newton's gravity.- 2.5 Covariance.- 2.5.1 Principle of General Covariance.- 2.5.2 Covariant Differentiation.- 2.5.3 Geodesic equation from covariance principle.- 2.5.4 Covariant divergence and conserved quantities.- 2.6 Riemann Curvature Tensor.- 2.6.1 Second covariant derivative of scalars and vectors.- 2.6.2 Symmetries of the Riemann tensor.- 2.6.3 Test for flatness.- 2.6.4 Second covariant derivative of tensors.- 2.6.5 Bianchi identities.- 2.6.6 Einstein tensor.- 2.7 Einstein's Field Equations.- 2.8 Relativistic Stars.- 2.8.1 Metric in static isotropic spacetime.- 2.8.2 The Schwarzschild solution.- 2.8.3 Riemann tensor outside a Schwarzschild star.- 2.8.4 Energy-Momentum tensor of matter.- 2.8.5 The Oppenheimer-Volkoff equations.- 2.8.6 Gravitational collapse and limiting mass.- 2.9 Action Principle in Gravity.- 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.- 3.4 Partial Decoupling of Matter from Gravity.- 3.5 Equations of Relativistic Stellar Structure.- 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 Stability.- 3.9.6 Nonrelativistic electron region.- 3.9.7 Relativistic electron region: asymptotic white dwarf mass.- 3.9.8 Nature of limiting mass of dwarfs and neutron stars.- 3.9.9 Degenerate ideal gas neutron star.- 3.10 Improvements in White Dwarf Models.- 3.10.1 Nature of matter at dwarf densities.- 3.10.2 Carbon and oxygen white dwarfs.- 3.11 Stellar Sequences from White Dwarfs to Neutron Stars.- 3.12 Star of Uniform Density.- 3.13 Baryon Number of a Star.- 3.14 Bound on Maximum Mass of Neutron Stars.- 3.15 Beyond Maximum-Mass Neutron Stars.- 3.16 Black Holes.- 3.16.1 Interior and Exterior Regions.- 3.16.2 No statics within.- 3.16.3 Black hole densities.- 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 vs. Renormalized Theory.- 4.13 Bound vs. Unbound Neutron Matter.- 4.13.1 Bound neutron matter.- 4.13.2 First-Order phase transition.- 4.14 Note on Dimensions.- 4.15 Summary.- 5 Neutron Stars.- 5.1 Introduction.- 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 Pulsar masses.- 5.2.9 Pulsar ages.- 5.2.10 Evolution of the braking index5.- 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 Neutron star matter.- 5.3.5 Hints for computation.- 5.3.6 Isospin- and charge-favored baryon species.- 5.3.7 Surface of neutron stars.- 5.3.8 Reprise of white dwarfs to neutron stars.- 5.3.9 Development of neutron star sequences.- 5.3.10 Mass as a function of central density.- 5.3.11 Radius-Mass characteristic relationship.- 5.4 Constitution of Neutron Stars.- 5.4.1 Limiting mass and the equation of state.- 5.4.2 Beta equilibrium and symmetry energy.- 5.4.3 Hyperon stars.- 5.4.4 Limiting mass and hyperon populations.- 5.4.5 Compression modulus and effective nucleon mass.- 5.4.6 Pion and kaon condensation.- 5.4.7 Charge neutrality achieved among baryons.- 5.5 Tables of Equations of State.- 5.5.1 Low density.- 5.5.2 High density.- 6 Rotating Neutron Stars.- 6.1 Motivation.- 6.2 Dragging of Local Inertial Frames.- 6.3 Interior Solution for the Dragging Frequency.- 6.4 Kepler Angular Velocity in General Relativity.- 6.5 Effect of Frame Dragging on Kepler Frequency.- 6.6 Hartle-Thorne Perturbative Solution.- 6.6.1 Comparison of Perturbative and Numerical Solutions.- 6.7 Imprint of Angular Momentum.- 6.8 Rotating Stars with Realistic Equations of State.- 6.9 Effect of Rotation on Stellar Structure.- 6.10 Gravitational-Wave Instabilities.- 7 Limiting Rotational Period 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 Discussion and Alternatives.- 7.8 Summary.- 8 Quark Stars.- 8.1 Introduction.- 8.2 Quark Matter Equation of State.- 8.2.1 Zero Temperature.- 8.2.2 Massless quark approximation.- 8.2.3 First order in ?s.- 8.3 Quark Star Matter.- 8.4 Strange and Charm Stars.- 8.5 Beyond White Dwarfs and Neutron Stars.- 9 Hybrid Stars.- 9.1 Introduction.- 9.2 Constant-Pressure Phase Transition.- 9.3 The Confined-Deconfined Phase Transition in Neutron Stars.- 9.3.1 Conservation laws are global-not local.- 9.4 Degrees of Freedom in a Multicomponent System.- 9.4.1 Coulomb lattice structure of the mixed phase.- 9.4.2 Phase diagram.- 9.4.3 Two energy scales.- 9.5 Gross Structure of a Hybrid Star.- 9.5.1 Energy budget in the reapportionment of charge.- 9.6 Crystalline Structure.- 9.6.1 Crystalline structure as a function of stellar mass.- 9.6.2 Possible implications for glitches.- 9.7 Mechanism for Formation of Low-Mass Black Holes.- 9.7.1 Hyperonization-Induced collapse.- 9.7.2 Deconfinement-Induced collapse.- 9.7.3 Density profiles.- 9.7.4 Discussion.- 9.8 Tables of Equation of State for Hybrid Stars.- 10 Strange Stars.- 10.1 The Strange Matter Hypothesis.- 10.2 Compatibility of the Hypothesis with Present Knowledge.- 10.2.1 Energetic considerations.- 10.2.2 The universe and its evolution.- 10.2.3 Stability of nuclei against decay to strange matter.- 10.2.4 Stability of nuclei to conversion by strange nuggets.- 10.2.5 Terrestrial searches.- 10.2.6 Summary, prospects and challenges.- 10.3 Submillisecond Pulsars.- 10.3.1 The fine-tuning problem.- 10.3.2 Limits to neutron star rotation.- 10.3.3 Implausibly high central densities.- 10.3.4 Strange stars as fast rotors.- 10.3.5 Out of the impasse.- 10.3.6 Motivation for searches and prospects for discovery.- 10.4 Structure of Strange Stars.- 10.5 Strange Stars to Strange Dwarfs.- 10.5.1 Strange stars with nuclear crusts.- 10.5.2 Strange dwarfs with nuclear crusts.- 10.5.3 Stability.- 10.5.4 Possible new class of dense white dwarfs.- 10.6 Conclusion.- Appendix A: Useful Astronomical Data.- Books for Further Study.- References.