Cover image for Basic relativity
Title:
Basic relativity
Author:
Mould, Richard A.
Personal Author:
Publication Information:
New York : Springer-Verlag, [1994]

©1994
Physical Description:
xiv, 452 pages : illustrations ; 25 cm
Language:
English
Subject Term:
ISBN:
9780387941882

9783540941880

9780387952109
Format :
Book

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

Prefacep. vii
Part I
1. Principles of Relativityp. 3
1.1 Galileo's Principlep. 3
1.2 A Century of Electricity and Magnetismp. 5
1.3 Maxwell's Equationsp. 7
1.4 Stellar Aberrationp. 8
1.5 The Michelson-Morley Experimentp. 8
1.6 The Trouton-Noble Experimentp. 13
Problemsp. 16
2. The Physical Argumentsp. 18
2.1 Physical Ideasp. 18
2.2 Some Applicationsp. 27
2.3 Velocity Additionp. 35
2.4 The Twin Paradoxp. 37
2.5 The Pole in the Barn Paradoxp. 40
2.6 Coordinate Frames of Referencep. 42
Problemsp. 44
3. The Algebraic and Graphic Argumentsp. 48
3.1 The Lorentz Transformationp. 48
3.2 Other Applicationsp. 51
3.3 Velocity Additionp. 55
3.4 The Invariant Intervalp. 57
3.5 The Minkowski Diagramp. 61
3.6 Use of the Minkowski Diagramp. 66
3.7 Four-Vectorsp. 71
3.8 Velocity and Acceleration Four-Vectorsp. 72
3.9 The Propagation Four-Vectorp. 75
3.10 Doppler Effectp. 78
3.11 Experimental Evidence--Kinematicsp. 81
Problemsp. 84
4. Mathematical Toolsp. 91
4.1 Matricesp. 91
4.2 The Lorentz Transformationp. 98
4.3 Vector Operatorsp. 100
4.4 Tensorsp. 103
4.5 The Metric Inequalityp. 107
Summaryp. 109
Problemsp. 110
5. Dynamicsp. 113
5.1 The Physical Assumptionsp. 114
5.2 The Euler-Lagrange Formalismp. 121
5.3 The Momentum Four-Vectorp. 125
5.4 The Four-Forcep. 127
5.5 Torquep. 134
5.6 Collisionsp. 136
5.7 Experimental Evidence--Dynamicsp. 142
Problemsp. 144
6. Electromagnetic Theoryp. 148
6.1 Electric and Magnetic Fieldsp. 148
6.2 Lorentz Forcep. 153
6.3 Moving Magnet Problemp. 157
6.4 Trouton-Noble Experimentp. 161
6.5 Maxwell's Equationsp. 163
6.6 Electromagnetic Potentialsp. 166
6.7 Energy-Momentum Tensorp. 168
Problemsp. 170
Part II
7. Differential Geometry Ip. 177
7.1 The Scalar Invariantp. 177
7.2 The Metric Tensorp. 178
7.3 Vectorsp. 181
7.4 The Rectilinear Casep. 183
7.5 The Polar Casep. 185
7.6 Contravariant Metric Tensorp. 190
7.7 Tensorsp. 191
Summary of Tensor Algebrap. 195
7.8 Parallel Displacementp. 196
7.9 The Geodesic Pathp. 204
7.10 Parallel Displacement of Covariant Vectorsp. 208
7.11 Covariant Derivativesp. 209
7.12 Space-Time Differential Geometryp. 213
Summary of Four-Vectorsp. 217
Problemsp. 218
8. Uniform Accelerationp. 221
8.1 Nonrigid Bodiesp. 221
8.2 Accelerating a Point Massp. 224
8.3 A Uniformly Accelerated Framep. 228
8.4 Uniformly Accelerated Coordinatesp. 231
8.5 The Matter of Metricp. 232
Summary of Metric Relationshipsp. 234
8.6 Kinematic Characteristics of the Systemp. 235
8.7 Falling Bodiesp. 241
8.8 Geodesic Pathsp. 244
8.9 Falling Clocksp. 249
8.10 A Supported Objectp. 252
8.11 Local Coordinatesp. 253
Summary of Kinematic Relationshipsp. 256
8.12 Dynamicsp. 257
8.13 Gravitational Force and Constants of Motionp. 261
Problemsp. 265
9. Rotation and the Electromagnetic Fieldp. 269
9.1 The Rotation Transformationp. 269
9.2 Physical Interpretationp. 271
9.3 The Geodesic Equationp. 273
9.4 Dynamicsp. 274
9.5 General Electromagnetic Fieldsp. 278
9.6 Nongeodesic Pathsp. 281
9.7 Generally Covariant Field Equationsp. 283
Problemsp. 284
10. The Material Mediump. 287
10.1 The Energy-Momentum Tensorp. 287
10.2 Dust Particlesp. 288
10.3 Ideal Gasp. 290
10.4 Internal Forcesp. 290
10.5 The Total Tensorp. 295
Problemsp. 296
11. Differential Geometry II: Curved Surfacesp. 298
11.1 A Spherical Surfacep. 298
11.2 A Curvature Criterionp. 304
11.3 Curvature Tensor on a Spherep. 306
11.4 Ricci Tensor and the Scalar Curvaturep. 307
Problemsp. 309
12. General Relativityp. 312
12.1 The Principle of Equivalencep. 313
12.2 Einstein's Field Equationp. 315
12.3 Evaluation of the Constantp. 318
12.4 The Schwarzschild Solutionp. 321
12.5 Kinematic Characteristics of the Fieldp. 324
12.6 Falling Bodiesp. 328
12.7 Four-Velocityp. 330
12.8 Dynamicsp. 330
12.9 Theory as Constructp. 338
12.10 Three Tests of General Relativityp. 339
12.11 New Tests and Challengesp. 344
Problemsp. 346
13. Astrophysicsp. 349
13.1 Compact Objectsp. 349
13.2 Black Holesp. 351
13.3 Rotating Black Holesp. 358
13.4 Evidence for Compact Objectsp. 368
13.5 Gravity Wavesp. 377
Problemsp. 388
14. Cosmologyp. 392
14.1 The Cosmological Principlep. 392
14.2 The Cosmological Constantp. 393
14.3 Three-Dimensional Hypersurfacep. 394
14.4 General Solution of the Field Equationp. 398
14.5 Einstein and de Sitter Solutionsp. 400
14.6 The Matter-Dominated Universep. 402
14.7 Critical Massp. 405
14.8 Measuring a Flat, Matter-Dominated Universep. 407
14.9 The Inflationary Universep. 416
Problemsp. 423
Appendixes
A. The Lorentz Transformationp. 425
B. Calculus of Variationsp. 427
C. The Geodesic Equationsp. 430
D. The Geodesic Equation in Coordinate Formp. 431
E. Uniformly Accelerated Transformation Equationsp. 432
F. The Riemann-Christoffel Curvature Tensorp. 434
G. Transformation to the Tangent Planep. 436
H. General Lorentz Transformation and the Stress Tensorp. 438
Answers to Selected Problemsp. 439
Referencesp. 443
Indexp. 445