Basic RelativitySpringer Science & Business Media, 1 nov 2001 - 452 pagina's This is a comprehensive textbook for advanced undergraduates and beginning graduate students in physics or astrophysics, developing both the formalism and the physical ideas of special and general relativity in a logical and coherent way. The book is in two parts. Part one focuses on the special theory and begins with the study of relativistic kinematics from three points of view: the physical (the classic gedanken experiments), the algebraic (the Lorentz transformations), and the graphic (the Minkowski diagrams). Part one concludes with chapters on relativistic dynamics and electrodynamics. Part two begins with a chapter introducing differential geometry to set the mathematical background for general relativity. The physical basis for the theory is begun in the chapter on uniform accelerations. Subsequent chapters cover rotation, the electromagnetic field, and material media. A second chapter on differential geometry provides the background for Einstein's gravitational-field equation and Schwarzschild's solution. The physical significance of this solution is examined together with the challenges to the theory that have been successfully met inside the solar system. Other applications follow in the final chapters on astronomy and cosmology: These include black holes, quasars, and gravity waves as well as the relativistic features of an expanding universe ¿ including a section on the inflationary model. |
Inhoudsopgave
Principle of Relativity | 3 |
12 A Century of Electricity and Magnetism | 5 |
13 Maxwells Equations | 7 |
14 Stellar Aberration | 8 |
16 The TroutonNoble Experiment | 13 |
The Physical Arguments | 18 |
22 Some Applications | 27 |
23 Velocity Addition | 35 |
Summary of Metric Relationships | 234 |
86 Kinematic Characteristics of the System | 235 |
87 Falling Bodies | 241 |
88 Geodesic Paths | 244 |
89 Falling Clocks | 249 |
810 A Supported Object | 252 |
811 Local Coordinates | 253 |
Summary of Kinematic Relationships | 256 |
24 The Twin Paradox | 37 |
25 The Pole in the Barn Paradox | 40 |
26 Coordinate Frames of Reference | 42 |
Problems | 44 |
The Algebraic and Graphic Arguments | 48 |
32 Other Applications | 51 |
33 Velocity Addition | 55 |
34 The Invariant Interval | 57 |
35 The Minkowski Diagram | 61 |
36 Use of the Minkowski Diagram | 66 |
37 FourVectors | 71 |
38 Velocity and Acceleration FourVectors | 72 |
39 The Propagation FourVector | 75 |
310 Doppler Effect | 78 |
311 Experimental EvidenceKinematics | 81 |
Problems | 84 |
Mathematical Tools | 91 |
42 The Lorentz Transformation | 98 |
43 Vector Operators | 100 |
44 Tensors | 103 |
45 The Metric Inequality | 107 |
Summary | 109 |
Problems | 110 |
Dynamics | 113 |
51 The Physical Assumptions | 114 |
52 The EulerLagrange Formalism | 121 |
53 The Momentum FourVector | 125 |
54 The FourForce | 127 |
55 Torque | 134 |
56 Collisions | 136 |
57 Experimental EvidenceDynamics | 142 |
Problems | 144 |
Electromagnetic Theory | 148 |
62 Lorentz Force | 153 |
63 Moving Magnet Problem | 157 |
64 TroutonNoble Experiment | 161 |
65 Maxwells Equations | 163 |
66 Electromagnetic Potentials | 166 |
67 EnergyMomentum Tensor | 168 |
Problems | 171 |
Part II | 175 |
Differential Geometry I | 177 |
72 The Metric Tensor | 178 |
73 Vectors | 181 |
74 The Rectilinear Case | 183 |
75 The Polar Case | 185 |
76 Contravariant Metric Tensor | 190 |
77 Tensors | 191 |
Summary of Tensor Algebra | 195 |
78 Parallel Displacement | 196 |
79 The Geodesic Path | 204 |
710 Parallel Displacement of Covariant Vectors | 208 |
711 Covariant Derivatives | 209 |
712 SpaceTime Differential Geometry | 213 |
Summary of Four Vectors | 217 |
Problems | 218 |
Uniform Acceleration | 221 |
82 Accelerating a Point Mass | 224 |
83 A Uniformly Accelerated Frame | 228 |
84 Uniformly Accelerated Coordinates | 231 |
85 The Matter of Metric | 232 |
812 Dynamics | 257 |
813 Gravitational Force and Constants of Motion | 261 |
Problems | 265 |
Rotation and the Electromagnetic Field | 269 |
92 Physical Interpretation | 271 |
93 The Geodesic Equation | 273 |
94 Dynamics | 274 |
95 General Electromagnetic Fields | 278 |
96 NonGeodesic Paths | 281 |
97 Generally Covariant Field Equations | 283 |
Problems | 284 |
The Material Medium | 287 |
102 Dust Particles | 288 |
103 Ideal Gas | 290 |
105 The Total Tensor | 295 |
Problems | 296 |
Differential Geometry II Curved Surfaces | 298 |
112 A Curvature Criterion | 304 |
113 Curvature Tensor on a Sphere | 306 |
114 Ricci Tensor and the Scalar Curvature | 307 |
Problems | 309 |
General Relativity | 312 |
121 The Principle of Equivalence | 313 |
122 Einsteins Field Equation | 315 |
123 Evaluation of the Constant | 318 |
124 The Schwarzschild Solution | 321 |
125 Kinematic Characteristics of the Field | 324 |
126 Falling Bodies | 328 |
127 FourVelocity | 330 |
129 Theory as Construct | 338 |
1210 Three Tests of General Relativity | 339 |
1211 New Tests and Challenges | 344 |
Problems | 346 |
Astrophysics | 349 |
132 Black Holes | 351 |
133 Rotating Black Holes | 358 |
134 Evidence for Compact Objects | 368 |
135 Gravity Waves | 377 |
Problems | 388 |
Cosmology | 392 |
142 The Cosmological Constant | 393 |
143 ThreeDimensional Hypersurface | 394 |
144 General Solution of the Field Equation | 398 |
145 Einstein and de Sitter Solutions | 400 |
146 The MatterDominated Universe | 402 |
147 Critical Mass | 405 |
148 Measuring a Flat MatterDominated Einsteinde Sitter Universe | 407 |
149 The Inflationary Universe | 416 |
Problems | 423 |
Appendixes | 425 |
B Calculus of Variations | 427 |
C The Geodesic Equation | 430 |
D The Geodesic Equation in Coordinate Form | 431 |
E Uniformly Accelerated Transformation Equations | 432 |
F The RiemannChristoffel Curvature Tensor | 434 |
G Transformation to the Tangent Plane | 436 |
H General Lorentz Transformation and the Stress Tensor | 438 |
Answers to Selected Problems | 439 |
References | 443 |
445 | |
Veelvoorkomende woorden en zinsdelen
angle black hole Chapter charge Christoffel symbols clock components conservation constant contravariant coordinate system coordinate values covariant curvature defined derivative direction distance dr² ds² Einstein electromagnetic energy energy-momentum tensor equal to zero equation in Eq event Example four-force four-vector four-velocity function galaxy geodesic equation given gives gravitational field horizon inertial system invariant interval inverse length Lorentz transformation magnetic field magnitude matrix meter stick metric tensor Minkowski diagram Minkowski space momentum motion moving neutron star nonrelativistic object observer origin parallel displaced particle path physical theorem polar coordinates potential principle Problem quantity radiation radius relativistic rest mass rest system result Ricci tensor scalar Schwarzschild Show shown in Figure space spacelike special relativity star stationary surface theory timelike torque transformation equations Trouton-Noble experiment uniformly accelerated system universe unprimed velocity of light wave world line x-axis