Basic Relativity

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Springer Science & Business Media, Dec 1, 2001 - Science - 452 pages
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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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Contents

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
Index
445
Copyright

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About the author (2001)

Mould, Department of Physics, State University of New York, Stony Brook.

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