Inhaltsangabe1 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 S