| Preface | p. vii |
| Introduction | p. 1 |
| Compact Stars | p. 2 |
| Compact Stars and Relativistic Physics | p. 5 |
| Compact Stars and Dense-Matter Physics | p. 6 |
| Special Relativity | p. 9 |
| Lorentz Invariance | p. 11 |
| Lorentz transformations | p. 11 |
| Time Dilation | p. 14 |
| Covariant vectors | p. 14 |
| Energy and Momentum | p. 16 |
| Energy-momentum tensor of a perfect fluid | p. 17 |
| Light cone | p. 18 |
| General Relativity | p. 19 |
| Scalars, Vectors, and Tensors in Curvilinear Coordinates | p. 20 |
| Photon in a gravitational field | p. 28 |
| Tidal gravity | p. 29 |
| Curvature of spacetime | p. 30 |
| Energy conservation and curvature | p. 30 |
| Gravity | p. 32 |
| Einstein's Discovery | p. 32 |
| Particle Motion in an Arbitrary Gravitational Field | p. 32 |
| Mathematical definition of local Lorentz frames | p. 35 |
| Geodesics | p. 36 |
| Comparison with Newton's gravity | p. 38 |
| Covariance | p. 39 |
| Principle of general covariance | p. 39 |
| Covariant differentiation | p. 40 |
| Geodesic equation from covariance principle | p. 41 |
| Covariant divergence and conserved quantities | p. 42 |
| Riemann Curvature Tensor | p. 45 |
| Second covariant derivative of scalars and vectors | p. 45 |
| Symmetries of the Riemann tensor | p. 46 |
| Test for flatness | p. 47 |
| Second covariant derivative of tensors | p. 47 |
| Bianchi identities | p. 48 |
| Einstein tensor | p. 48 |
| Einstein's Field Equations | p. 50 |
| Relativistic Stars | p. 52 |
| Metric in static isotropic spacetime | p. 53 |
| The Schwarzschild solution | p. 54 |
| Riemann tensor outside a Schwarzschild star | p. 55 |
| Energy-Momentum tensor of matter | p. 56 |
| The Oppenheimer-Volkoff equations | p. 57 |
| Gravitational collapse and limiting mass | p. 62 |
| Action Principle in Gravity | p. 63 |
| Derivations | p. 65 |
| Problems for Chapter 3 | p. 68 |
| Compact Stars: From Dwarfs to Black Holes | p. 70 |
| Birth and Death of Stars | p. 70 |
| Aim of this Chapter | p. 78 |
| Gravitational Units and Neutron Star Size | p. 79 |
| Units | p. 79 |
| Size and number of baryons in a star | p. 82 |
| Gravitational energy of a neutron star | p. 84 |
| Partial Decoupling of Matter from Gravity | p. 85 |
| Equations of Relativistic Stellar Structure | p. 87 |
| Interpretation | p. 87 |
| Boundary conditions and stellar sequences | p. 90 |
| Electrical Neutrality of Stars | p. 92 |
| "Constancy" of the Chemical Potential | p. 93 |
| Gravitational Redshift | p. 95 |
| Integrity of an atom in strong fields | p. 95 |
| Redshift in a general static field | p. 96 |
| Comparison of emitted and received light | p. 100 |
| Measurements of M/R from redshift | p. 100 |
| White Dwarfs and Neutron Stars | p. 101 |
| Overview | p. 101 |
| Fermi-Gas equation of state for nucleons and electrons | p. 103 |
| High and low-density limits | p. 109 |
| Polytropes and Newtonian white dwarfs | p. 112 |
| Nonrelativistic electron region | p. 116 |
| Ultrarelativistic electron region: asymptotic white dwarf mass | p. 116 |
| Nature of limiting mass of dwarfs and neutron stars | p. 120 |
| Degenerate ideal gas neutron star | p. 121 |
| Improvements in White Dwarf Models | p. 123 |
| Nature of matter at dwarf and neutron star densities | p. 123 |
| Low-density equation of state | p. 126 |
| Carbon and oxygen white dwarfs | p. 127 |
| Temperature and Neutron Star Surface | p. 130 |
| Stellar Sequences from White Dwarfs to Neutron Stars | p. 133 |
| Density Distribution in Neutron Stars | p. 136 |
| Baryon Number of a Star | p. 137 |
| Binding Energy of a Neutron Star | p. 138 |
| Star of Uniform Density | p. 140 |
| Scaling Solution of the OV Equations | p. 142 |
| Bound on Maximum Mass of Neutron Stars | p. 144 |
| Stability | p. 148 |
| Necessary condition for stability | p. 149 |
| Normal modes of vibration: Sufficient condition for stability | p. 151 |
| Beyond the Maximum-Mass Neutron Star | p. 152 |
| Hyperons and Quarks in Neutron Stars | p. 155 |
| First Order Phase Transitions in Stars | p. 156 |
| Degrees of freedom and driving forces | p. 157 |
| Isospin symmetry energy as a driving force | p. 159 |
| Geometrical phases | p. 162 |
| Color-flavor locked quark-matter phase (CFL) | p. 162 |
| Signal of Quark Deconfinement in Neutron Stars | p. 165 |
| Neutron Star Twins | p. 171 |
| Particle populations in twins | p. 173 |
| Test for stability | p. 174 |
| Formation and detection | p. 175 |
| Black Holes | p. 176 |
| Interior and exterior regions | p. 176 |
| No statics within | p. 179 |
| Black hole densities | p. 182 |
| Black Hole Evaporation | p. 182 |
| Kerr Metric for Rotating Black Hole | p. 183 |
| Problems for Chapter 4 | p. 184 |
| Cosmology | p. 187 |
| Foreword | p. 187 |
| Units and Data | p. 188 |
| World Lines and Weyl's Hypothesis | p. 188 |
| Metric for a uniform isotropic universe | p. 189 |
| Friedmann-Lemaitre Equations | p. 190 |
| Temperature Variation with Expansion | p. 192 |
| Expansion in the Three Ages | p. 192 |
| Redshift | p. 194 |
| Hubble constant and Universe age | p. 194 |
| Evolution of the Early Universe | p. 195 |
| Temperature and Density of the Early Universe | p. 196 |
| Derivation of the Planck Scale | p. 197 |
| Time-scale of Neutrino Interactions | p. 198 |
| Neutrino Reaction Time-scale Becomes Longer than the Age of the Universe | p. 198 |
| Ionization of Hydrogen | p. 199 |
| Present Photon and Baryon Densities | p. 199 |
| Expansion Since Equality of Radiation and Mass | p. 200 |
| Helium Abundance | p. 201 |
| Helium Abundance is Primeval | p. 201 |
| Redshift and Scale Factor Relationship | p. 201 |
| Collapse Time of a Dust Cloud | p. 202 |
| Jeans Mass | p. 203 |
| Jeans Mass in the Radiation Era | p. 203 |
| Jeans Mass in the Matter Era | p. 204 |
| Early Matter Dominated Universe | p. 205 |
| Curvature | p. 206 |
| Acceleration | p. 207 |
| References | p. 209 |
| Index | p. 217 |
| Table of Contents provided by Ingram. All Rights Reserved. |
