| Preface | p. vii |
| |
| Principles of Relativity | p. 3 |
| Galileo's Principle | p. 3 |
| A Century of Electricity and Magnetism | p. 5 |
| Maxwell's Equations | p. 7 |
| Stellar Aberration | p. 8 |
| The Michelson-Morley Experiment | p. 8 |
| The Trouton-Noble Experiment | p. 13 |
| Problems | p. 16 |
| The Physical Arguments | p. 18 |
| Physical Ideas | p. 18 |
| Some Applications | p. 27 |
| Velocity Addition | p. 35 |
| The Twin Paradox | p. 37 |
| The Pole in the Barn Paradox | p. 40 |
| Coordinate Frames of Reference | p. 42 |
| Problems | p. 44 |
| The Algebraic and Graphic Arguments | p. 48 |
| The Lorentz Transformation | p. 48 |
| Other Applications | p. 51 |
| Velocity Addition | p. 55 |
| The Invariant Interval | p. 57 |
| The Minkowski Diagram | p. 61 |
| Use of the Minkowski Diagram | p. 66 |
| Four-Vectors | p. 71 |
| Velocity and Acceleration Four-Vectors | p. 72 |
| The Propagation Four-Vector | p. 75 |
| Doppler Effect | p. 78 |
| Experimental Evidence--Kinematics | p. 81 |
| Problems | p. 84 |
| Mathematical Tools | p. 91 |
| Matrices | p. 91 |
| The Lorentz Transformation | p. 98 |
| Vector Operators | p. 100 |
| Tensors | p. 103 |
| The Metric Inequality | p. 107 |
| Summary | p. 109 |
| Problems | p. 110 |
| Dynamics | p. 113 |
| The Physical Assumptions | p. 114 |
| The Euler-Lagrange Formalism | p. 121 |
| The Momentum Four-Vector | p. 125 |
| The Four-Force | p. 127 |
| Torque | p. 134 |
| Collisions | p. 136 |
| Experimental Evidence--Dynamics | p. 142 |
| Problems | p. 144 |
| Electromagnetic Theory | p. 148 |
| Electric and Magnetic Fields | p. 148 |
| Lorentz Force | p. 153 |
| Moving Magnet Problem | p. 157 |
| Trouton-Noble Experiment | p. 161 |
| Maxwell's Equations | p. 163 |
| Electromagnetic Potentials | p. 166 |
| Energy-Momentum Tensor | p. 168 |
| Problems | p. 170 |
| |
| Differential Geometry I | p. 177 |
| The Scalar Invariant | p. 177 |
| The Metric Tensor | p. 178 |
| Vectors | p. 181 |
| The Rectilinear Case | p. 183 |
| The Polar Case | p. 185 |
| Contravariant Metric Tensor | p. 190 |
| Tensors | p. 191 |
| Summary of Tensor Algebra | p. 195 |
| Parallel Displacement | p. 196 |
| The Geodesic Path | p. 204 |
| Parallel Displacement of Covariant Vectors | p. 208 |
| Covariant Derivatives | p. 209 |
| Space-Time Differential Geometry | p. 213 |
| Summary of Four-Vectors | p. 217 |
| Problems | p. 218 |
| Uniform Acceleration | p. 221 |
| Nonrigid Bodies | p. 221 |
| Accelerating a Point Mass | p. 224 |
| A Uniformly Accelerated Frame | p. 228 |
| Uniformly Accelerated Coordinates | p. 231 |
| The Matter of Metric | p. 232 |
| Summary of Metric Relationships | p. 234 |
| Kinematic Characteristics of the System | p. 235 |
| Falling Bodies | p. 241 |
| Geodesic Paths | p. 244 |
| Falling Clocks | p. 249 |
| A Supported Object | p. 252 |
| Local Coordinates | p. 253 |
| Summary of Kinematic Relationships | p. 256 |
| Dynamics | p. 257 |
| Gravitational Force and Constants of Motion | p. 261 |
| Problems | p. 265 |
| Rotation and the Electromagnetic Field | p. 269 |
| The Rotation Transformation | p. 269 |
| Physical Interpretation | p. 271 |
| The Geodesic Equation | p. 273 |
| Dynamics | p. 274 |
| General Electromagnetic Fields | p. 278 |
| Nongeodesic Paths | p. 281 |
| Generally Covariant Field Equations | p. 283 |
| Problems | p. 284 |
| The Material Medium | p. 287 |
| The Energy-Momentum Tensor | p. 287 |
| Dust Particles | p. 288 |
| Ideal Gas | p. 290 |
| Internal Forces | p. 290 |
| The Total Tensor | p. 295 |
| Problems | p. 296 |
| Differential Geometry II: Curved Surfaces | p. 298 |
| A Spherical Surface | p. 298 |
| A Curvature Criterion | p. 304 |
| Curvature Tensor on a Sphere | p. 306 |
| Ricci Tensor and the Scalar Curvature | p. 307 |
| Problems | p. 309 |
| General Relativity | p. 312 |
| The Principle of Equivalence | p. 313 |
| Einstein's Field Equation | p. 315 |
| Evaluation of the Constant | p. 318 |
| The Schwarzschild Solution | p. 321 |
| Kinematic Characteristics of the Field | p. 324 |
| Falling Bodies | p. 328 |
| Four-Velocity | p. 330 |
| Dynamics | p. 330 |
| Theory as Construct | p. 338 |
| Three Tests of General Relativity | p. 339 |
| New Tests and Challenges | p. 344 |
| Problems | p. 346 |
| Astrophysics | p. 349 |
| Compact Objects | p. 349 |
| Black Holes | p. 351 |
| Rotating Black Holes | p. 358 |
| Evidence for Compact Objects | p. 368 |
| Gravity Waves | p. 377 |
| Problems | p. 388 |
| Cosmology | p. 392 |
| The Cosmological Principle | p. 392 |
| The Cosmological Constant | p. 393 |
| Three-Dimensional Hypersurface | p. 394 |
| General Solution of the Field Equation | p. 398 |
| Einstein and de Sitter Solutions | p. 400 |
| The Matter-Dominated Universe | p. 402 |
| Critical Mass | p. 405 |
| Measuring a Flat, Matter-Dominated Universe | p. 407 |
| The Inflationary Universe | p. 416 |
| Problems | p. 423 |
| Appendixes | |
| The Lorentz Transformation | p. 425 |
| Calculus of Variations | p. 427 |
| The Geodesic Equations | p. 430 |
| The Geodesic Equation in Coordinate Form | p. 431 |
| Uniformly Accelerated Transformation Equations | p. 432 |
| The Riemann-Christoffel Curvature Tensor | p. 434 |
| Transformation to the Tangent Plane | p. 436 |
| General Lorentz Transformation and the Stress Tensor | p. 438 |
| Answers to Selected Problems | p. 439 |
| References | p. 443 |
| Index | p. 445 |
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