Preface PART I SPACE AND TIME IN NEWTONIAN PHYSICS AND SPECIAL RELATIVITY 1 Gravitational Physics 2 Geometry as Physics 2.1 Gravity Is Geometry 2.2 Experiments in Geometry 2.3 Different Geometries 2.4 Specifying Geometry 2.5 Coordinates and Line Element 2.6 Coordinates and Invariance 3 Space， Time， and Gravity in Newtonian Physics 3.1 Inertial Frames 3.2 The Principle of Relativity 3.3 Newtonian Gravity 3.4 Gravitational and Inertial Mass 3.5 Variational Principle for Newtonian Mechanics 4 Principles of Special Relativity 4.1 The Addition of Velocities and the Michelson-Morley Experiment 4.2 Einsteins Resolution and Its Consequences 4.3 Spacetime 4.4 Time Dilation and the Twin Paradox 4.5 Lorentz Boosts 4.6 Units 5 Special Relativistic Mechanics 5.1 Four-Vectors 5.2 Special Relativistic Kinematics 5.3 Special Relativistic Dynamics 5.4 Variational Principle for Free Particle Motion 5.5 Light Rays 5.6 Observers and Observations PART Ⅱ THE CURVED SPACETIMES OF GENERAL RELATIVITY 6 Gravity as Geometry 6.1 Testing the Equality of Gravitational and Inertial Mass 6.2 The Equivalence Principle 6.3 Clocks in a Gravitational Field 6.4 The Global Positioning System 6.5 Spacetime Is Curved 6.6 Newtonian Gravity in Spacetime Terms 7 The Description of Curved Spacetime 7.1 Coordinates 7.2 Metric 7.3 The Summation Convention 7.4 Local Inertial Frames 7.5 Light Cones and World Lines 7.6 Length， Area， Volume， and Four-Volume for Diagon Metrics 7.7 Embedding Diagrams and Wormholes 7.8 Vectors in Curved Spacetime 7.9 Three-Dimensional Surfaces in Four-Dimensional Spacetime 8 Geodesics 8.1 The Geodesic Equation 8.2 Solving the Geodesic Equation——-Symmetries and Conservation Laws 8.3 Null Geodesics 8.4 Local Inertial Frames and Freely Falling Frames 9 The Geometry Outside a Spherical Star 9.1 Schwarzschild Geometry 9.2 The Gravitational Redshift 9.3 Particle Orbits——Precession of the Perihelion 9.4 Light Ray Orbits——The Deflection and Time Delay of Light 10 Solar System Tests of General Relativity 10.1 Gravitational Redshift 10.2 PPN Parameters 10.3 Measurements of the PPN Parametery 10.4 Measurement of the PPN Parameter B-Precession of Mercurys Perihelion 11 Relativistic Gravity in Action 11.1 Gravitational Lensing 11.2 Accretion Disks Around Compact Objects 11.3 Binary Pulsars 12 Gravitational Collapse and Black Holes 12.1 The Schwarzschild Black Hole 12.2 Collapse to a Black Hole 12.3 Kruskal-Szekeres Coordinates 12.4 Nonspherical Gravitational Collapse 13 Astrophysical Black Holes 13.1 Black Holes in X-Ray Binaries 13.2 Black Holes in Galaxy Centers 13.3 Quantum Evaporation of Black Holes——Hawking Radiation 14 A Little Rotation 14.1 Rotational Dragging of Inertial Frames 14.2 Gyroscopes in Curved Spacetime 14.3 Geodetic Precession 14.4 Spacetime Outside a Slowly Rotating Spherical Body 14.5 Gyroscopes in the Spacetime of a Slowly Rotating Body 14.6 Gyros and Freely Falling Frames 15 Rotating Black Holes 15.1 Cosmic Censorship 15.2 The Kerr Geometry 15.3 The Horizon of a Rotating Black Hole 15.4 Orbits in the Equatorial Plane 15.5 The Ergosphere 16 Gravitational Waves 16.1 A Linearized Gravitational Wave 16.2 Detecting Gravitational Waves 16.3 Gravitational Wave Polarization 16.4 Gravitational Wave Interferometers 16.5 The Energy in Gravitational Waves 17 The Universe Observed 17.1 The Composition of the Universe 17.2 The Expanding Universe 17.3 Mapping the Universe 18 Cosmological Models 18.1 Homogeneous， Isotropic Spacetimes 18.2 The Cosmological Redshift 18.3 Matter， Radiation， and Vacuum 18.4 Evolution of the Flat FRW Models 18.5 The Big Bang and Age and Size of the Universe 18.6 Spatially Curved Robertson-Walker Metrics 18.7 Dynamics of the Universe 19 Which Universe and Why？ 19.1 Surveying the Universe 19.2 Explaining the Universe PART III THE EINSTEIN EQUATION 20 A Little More Math 20.1 Vectors 20.2 Dual Vectors 20.3 Tensors 20.4 The Covariant Derivative 20.5 Freely Falling Frames Again 21 Curvature and the Einstein Equation 21.1 Tidal Gravitational Forces 21.2 Equation of Geodesic Deviation 21.3 Riemann Curvature 21.4 The Einstein Equation in Vacuum 21.5 Linearized Gravity 22 The Source of Curvature 22.1 Densities 22.2 Conservation 22.2 Conservation of Energy-Momentum 22.3 The Einstein Equation 22.4 The Newtonian Limit 23 Gravitational Wave Emission 23.1 The Linearized Einstein Equation with Sources 23.2 Solving the Wave Equation with a Source 23.3 The General Solution of Linearized Gravity 23.4 Production of Weak Gravitational Waves 23.5 Gravitational Radiation from Binary Stars 23.6 The Quadrupole Formula for the Energy Loss in Gravitational Waves 23.7 Effects of Gravitational Radiation Detected in a Binary Pulsar 23.8 Strong Source Expectations 24 Relativistic Stars 24.1 The Power of the Pauli Principle 24.2 Relativistic Hydrostatic Equilibrium 24.3 Stellar Models 24.4 Matter in Its Ground State 24.5 Stability 24.6 Bounds on the Maximum Mass of Neutron Stars APPENDIXES A Units A.1 Units in General A.2 Units Employed in this Book B Curvature Quantities C Curvature and the Einstein Equation D Pedagogical Strategy D.1 Pedagogical Principles D.2 Organization D.3 Constructing Courses Bibliography Index
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