Basic Relativity

By: Richard A. Mould

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Paperback | 1 December 2001 | Edition Number 2

At a Glance

Paperback
468 Pages

Edition Type
Revised

Dimensions(cm)
23.39 x 15.6 x 2.39

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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.

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Non-Fiction Science Physics Relativity Physics Classical Mathematics Gravity Astronomy, Space & Time Applied Physics Astrophysics

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
Table of Contents provided by Syndetics. All Rights Reserved.

Basic Relativity

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