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| Preface | |
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| Space and Time in Newtonian Physics and Special Relativity | |
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| Gravitational Physics | |
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| Geometry as Physics | |
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| Gravity Is Geometry | |
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| Experiments in Geometry | |
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| Different Geometries | |
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| Specifying Geometry | |
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| Coordinates and Line Element | |
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| Coordinates and Invariance | |
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| Space, Time, and Gravity in Newtonian Physics | |
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| Inertial Frames | |
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| The Principle of Relativity | |
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| Newtonian Gravity | |
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| Gravitational and Inertial Mass | |
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| Variational Principle for Newtonian Mechanics | |
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| Principles of Special Relativity | |
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| The Addition of Velocities and the Michelson-Morley Experiment | |
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| Einstein's Resolution and Its Consequences | |
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| Spacetime | |
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| Time Dilation and the Twin Paradox | |
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| Lorentz Boosts | |
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| Units | |
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| Special Relativistic Mechanics | |
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| Four-Vectors | |
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| Special Relativistic Kinematics | |
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| Special Relativistic Dynamics | |
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| Variational Principle for Free Particle Motion | |
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| Light Rays | |
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| Observers and Observations | |
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| The Curved Spacetimes of General Relativity | |
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| Gravity as Geometry | |
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| Testing the Equality of Gravitational and Inertial Mass | |
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| The Equivalence Principle | |
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| Clocks in a Gravitational Field | |
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| The Global Positioning System | |
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| Spacetime Is Curved | |
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| Newtonian Gravity in Spacetime Terms | |
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| The Description of Curved Spacetime | |
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| Coordinates | |
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| Metric | |
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| The Summation Convention | |
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| Local Inertial Frames | |
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| Light Cones and World Lines | |
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| Length, Area, Volume, and Four-Volume for Diagonal Metrics | |
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| Embedding Diagrams and Wormholes | |
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| Vectors in Curved Spacetime | |
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| Three-Dimensional Surfaces in Four-Dimensional Spacetime | |
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| Geodesics | |
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| The Geodesic Equation | |
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| Solving the Geodesic Equation--Symmetries and Conservation Laws | |
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| Null Geodesics | |
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| Local Inertial Frames and Freely Falling Frames | |
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| The Geometry Outside a Spherical Star | |
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| Schwarzschild Geometry | |
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| The Gravitational Redshift | |
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| Particle Orbits--Precession of the Perihelion | |
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| Light Ray Orbits--The Deflection and Time Delay of Light | |
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| Solar System Tests of General Relativity | |
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| Gravitational Redshift | |
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| PPN Parameters | |
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| Measurements of the PPN Parameter [gamma] | |
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| Measurement of the PPN Parameter [beta]--Precession of Mercury's Perihelion | |
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| Relativistic Gravity in Action | |
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| Gravitational Lensing | |
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| Accretion Disks Around Compact Objects | |
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| Binary Pulsars | |
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| Gravitational Collapse and Black Holes | |
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| The Schwarzschild Black Hole | |
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| Collapse to a Black Hole | |
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| Kruskal-Szekeres Coordinates | |
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| Nonspherical Gravitational Collapse | |
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| Astrophysical Black Holes | |
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| Black Holes in X-Ray Binaries | |
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| Black Holes in Galaxy Centers | |
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| Quantum Evaporation of Black Holes--Hawking Radiation | |
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| A Little Rotation | |
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| Rotational Dragging of Inertial Frames | |
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| Gyroscopes in Curved Spacetime | |
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| Geodetic Precession | |
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| Spacetime Outside a Slowly Rotating Spherical Body | |
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| Gyroscopes in the Spacetime of a Slowly Rotating Body | |
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| Gyros and Freely Falling Frames | |
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| Rotating Black Holes | |
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| Cosmic Censorship | |
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| The Kerr Geometry | |
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| The Horizon of a Rotating Black Hole | |
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| Orbits in the Equatorial Plane | |
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| The Ergosphere | |
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| Gravitational Waves | |
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| A Linearized Gravitational Wave | |
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| Detecting Gravitational Waves | |
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| Gravitational Wave Polarization | |
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| Gravitational Wave Interferometers | |
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| The Energy in Gravitational Waves | |
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| The Universe Observed | |
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| The Composition of the Universe | |
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| The Expanding Universe | |
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| Mapping the Universe | |
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| Cosmological Models | |
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| Homogeneous, Isotropic Spacetimes | |
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| The Cosmological Redshift | |
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| Matter, Radiation, and Vacuum | |
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| Evolution of the Flat FRW Models | |
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| The Big Bang and Age and Size of the Universe | |
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| Spatially Curved Robertson-Walker Metrics | |
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| Dynamics of the Universe | |
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| Which Universe and Why? | |
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| Surveying the Universe | |
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| Explaining the Universe | |
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| The Einstein Equation | |
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| A Little More Math | |
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| Vectors | |
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| Dual Vectors | |
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| Tensors | |
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| The Covariant Derivative | |
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| Freely Falling Frames Again | |
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| Curvature and the Einstein Equation | |
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| Tidal Gravitational Forces | |
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| Equation of Geodesic Deviation | |
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| Riemann Curvature | |
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| The Einstein Equation in Vacuum | |
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| Linearized Gravity | |
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| The Source of Curvature | |
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| Densities | |
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| Conservation | |
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| Conservation of Energy-Momentum | |
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| The Einstein Equation | |
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| The Newtonian Limit | |
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| Gravitational Wave Emission | |
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| The Linearized Einstein Equation with Sources | |
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| Solving the Wave Equation with a Source | |
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| The General Solution of Linearized Gravity | |
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| Production of Weak Gravitational Waves | |
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| Gravitational Radiation from Binary Stars | |
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| The Quadrupole Formula for the Energy Loss in Gravitational Waves | |
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| Effects of Gravitational Radiation Detected in a Binary Pulsar | |
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| Strong Source Expectations | |
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| Relativistic Stars | |
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| The Power of the Pauli Principle | |
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| Relativistic Hydrostatic Equilibrium | |
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| Stellar Models | |
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| Matter in Its Ground State | |
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| Stability | |
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| Bounds on the Maximum Mass of Neutron Stars | |
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| Appendixes | |
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| Units | |
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| Units in General | |
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| Units Employed in this Book | |
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| Curvature Quantities | |
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| Curvature and the Einstein Equation | |
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| Pedagogical Strategy | |
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| Pedagogical Principles | |
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| Organization | |
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| Constructing Courses | |
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| Bibliography | |
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| Index | |