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Searching... | QC173.55 .M68 1994 | Adult Non-Fiction | Non-Fiction Area | Searching... | Searching... |

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### Summary

### Summary

This comprehensive textbook develops in a logical and coherent way both the formalism and the physical ideas of special and general relativity. Part one focuses on the special theory and begins with the study of relativistic kinematics from three points of view. Part two begins with a chapter introducing differential geometry. 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 book is aimed at advanced undergraduates and beginning graduate students in physics or astrophysics.

### Reviews 1

### Choice Review

Mould writes on the special and general theories of relativity and their applications in astrophysics and cosmology. What is unusual about this book is the insistence on clarity at the fundamental level, especially in regard to the geometry of accelerated and rotating coordinate systems and the gravitational field. The good aspects of this insistence are obvious; the trouble is that the student is required to absorb an immense amount of mathematical detail, some of it quite subtle, without ever being shown what it is for. The problems help, but the first bit of experimental evidence is found on p. 81, and the reader is neither shown the theories of three of the four fundamental tests of general relativity nor invited to work them out. Formulas occasionally appear from nowhere, to be justified, not derived, and the phrase "it can be shown" occurs with embarrassing frequency. On the other hand, a large number of worked examples clarify the explanations, and when, after long preparation, readers arrive at black holes, gravity waves, and cosmology, they will understand at the geometrical level what many understand only with formulas. Strongly recommended on this account, but with reservations as an introduction. For senior undergraduates and first-year graduate students. D. Park; emeritus, Williams College

### Table of Contents

Preface | p. vii |

Part I | |

1. Principles of Relativity | p. 3 |

1.1 Galileo's Principle | p. 3 |

1.2 A Century of Electricity and Magnetism | p. 5 |

1.3 Maxwell's Equations | p. 7 |

1.4 Stellar Aberration | p. 8 |

1.5 The Michelson-Morley Experiment | p. 8 |

1.6 The Trouton-Noble Experiment | p. 13 |

Problems | p. 16 |

2. The Physical Arguments | p. 18 |

2.1 Physical Ideas | p. 18 |

2.2 Some Applications | p. 27 |

2.3 Velocity Addition | p. 35 |

2.4 The Twin Paradox | p. 37 |

2.5 The Pole in the Barn Paradox | p. 40 |

2.6 Coordinate Frames of Reference | p. 42 |

Problems | p. 44 |

3. The Algebraic and Graphic Arguments | p. 48 |

3.1 The Lorentz Transformation | p. 48 |

3.2 Other Applications | p. 51 |

3.3 Velocity Addition | p. 55 |

3.4 The Invariant Interval | p. 57 |

3.5 The Minkowski Diagram | p. 61 |

3.6 Use of the Minkowski Diagram | p. 66 |

3.7 Four-Vectors | p. 71 |

3.8 Velocity and Acceleration Four-Vectors | p. 72 |

3.9 The Propagation Four-Vector | p. 75 |

3.10 Doppler Effect | p. 78 |

3.11 Experimental Evidence--Kinematics | p. 81 |

Problems | p. 84 |

4. Mathematical Tools | p. 91 |

4.1 Matrices | p. 91 |

4.2 The Lorentz Transformation | p. 98 |

4.3 Vector Operators | p. 100 |

4.4 Tensors | p. 103 |

4.5 The Metric Inequality | p. 107 |

Summary | p. 109 |

Problems | p. 110 |

5. Dynamics | p. 113 |

5.1 The Physical Assumptions | p. 114 |

5.2 The Euler-Lagrange Formalism | p. 121 |

5.3 The Momentum Four-Vector | p. 125 |

5.4 The Four-Force | p. 127 |

5.5 Torque | p. 134 |

5.6 Collisions | p. 136 |

5.7 Experimental Evidence--Dynamics | p. 142 |

Problems | p. 144 |

6. Electromagnetic Theory | p. 148 |

6.1 Electric and Magnetic Fields | p. 148 |

6.2 Lorentz Force | p. 153 |

6.3 Moving Magnet Problem | p. 157 |

6.4 Trouton-Noble Experiment | p. 161 |

6.5 Maxwell's Equations | p. 163 |

6.6 Electromagnetic Potentials | p. 166 |

6.7 Energy-Momentum Tensor | p. 168 |

Problems | p. 170 |

Part II | |

7. Differential Geometry I | p. 177 |

7.1 The Scalar Invariant | p. 177 |

7.2 The Metric Tensor | p. 178 |

7.3 Vectors | p. 181 |

7.4 The Rectilinear Case | p. 183 |

7.5 The Polar Case | p. 185 |

7.6 Contravariant Metric Tensor | p. 190 |

7.7 Tensors | p. 191 |

Summary of Tensor Algebra | p. 195 |

7.8 Parallel Displacement | p. 196 |

7.9 The Geodesic Path | p. 204 |

7.10 Parallel Displacement of Covariant Vectors | p. 208 |

7.11 Covariant Derivatives | p. 209 |

7.12 Space-Time Differential Geometry | p. 213 |

Summary of Four-Vectors | p. 217 |

Problems | p. 218 |

8. Uniform Acceleration | p. 221 |

8.1 Nonrigid Bodies | p. 221 |

8.2 Accelerating a Point Mass | p. 224 |

8.3 A Uniformly Accelerated Frame | p. 228 |

8.4 Uniformly Accelerated Coordinates | p. 231 |

8.5 The Matter of Metric | p. 232 |

Summary of Metric Relationships | p. 234 |

8.6 Kinematic Characteristics of the System | p. 235 |

8.7 Falling Bodies | p. 241 |

8.8 Geodesic Paths | p. 244 |

8.9 Falling Clocks | p. 249 |

8.10 A Supported Object | p. 252 |

8.11 Local Coordinates | p. 253 |

Summary of Kinematic Relationships | p. 256 |

8.12 Dynamics | p. 257 |

8.13 Gravitational Force and Constants of Motion | p. 261 |

Problems | p. 265 |

9. Rotation and the Electromagnetic Field | p. 269 |

9.1 The Rotation Transformation | p. 269 |

9.2 Physical Interpretation | p. 271 |

9.3 The Geodesic Equation | p. 273 |

9.4 Dynamics | p. 274 |

9.5 General Electromagnetic Fields | p. 278 |

9.6 Nongeodesic Paths | p. 281 |

9.7 Generally Covariant Field Equations | p. 283 |

Problems | p. 284 |

10. The Material Medium | p. 287 |

10.1 The Energy-Momentum Tensor | p. 287 |

10.2 Dust Particles | p. 288 |

10.3 Ideal Gas | p. 290 |

10.4 Internal Forces | p. 290 |

10.5 The Total Tensor | p. 295 |

Problems | p. 296 |

11. Differential Geometry II: Curved Surfaces | p. 298 |

11.1 A Spherical Surface | p. 298 |

11.2 A Curvature Criterion | p. 304 |

11.3 Curvature Tensor on a Sphere | p. 306 |

11.4 Ricci Tensor and the Scalar Curvature | p. 307 |

Problems | p. 309 |

12. General Relativity | p. 312 |

12.1 The Principle of Equivalence | p. 313 |

12.2 Einstein's Field Equation | p. 315 |

12.3 Evaluation of the Constant | p. 318 |

12.4 The Schwarzschild Solution | p. 321 |

12.5 Kinematic Characteristics of the Field | p. 324 |

12.6 Falling Bodies | p. 328 |

12.7 Four-Velocity | p. 330 |

12.8 Dynamics | p. 330 |

12.9 Theory as Construct | p. 338 |

12.10 Three Tests of General Relativity | p. 339 |

12.11 New Tests and Challenges | p. 344 |

Problems | p. 346 |

13. Astrophysics | p. 349 |

13.1 Compact Objects | p. 349 |

13.2 Black Holes | p. 351 |

13.3 Rotating Black Holes | p. 358 |

13.4 Evidence for Compact Objects | p. 368 |

13.5 Gravity Waves | p. 377 |

Problems | p. 388 |

14. Cosmology | p. 392 |

14.1 The Cosmological Principle | p. 392 |

14.2 The Cosmological Constant | p. 393 |

14.3 Three-Dimensional Hypersurface | p. 394 |

14.4 General Solution of the Field Equation | p. 398 |

14.5 Einstein and de Sitter Solutions | p. 400 |

14.6 The Matter-Dominated Universe | p. 402 |

14.7 Critical Mass | p. 405 |

14.8 Measuring a Flat, Matter-Dominated Universe | p. 407 |

14.9 The Inflationary Universe | p. 416 |

Problems | p. 423 |

Appendixes | |

A. The Lorentz Transformation | p. 425 |

B. Calculus of Variations | p. 427 |

C. The Geodesic Equations | p. 430 |

D. The Geodesic Equation in Coordinate Form | p. 431 |

E. Uniformly Accelerated Transformation Equations | p. 432 |

F. The Riemann-Christoffel Curvature Tensor | p. 434 |

G. Transformation to the Tangent Plane | p. 436 |

H. General Lorentz Transformation and the Stress Tensor | p. 438 |

Answers to Selected Problems | p. 439 |

References | p. 443 |

Index | p. 445 |