The Geometry of Spacetime: An Introduction to Special and General Relativity / Edition 1

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In 1905, Albert Einstein offered a revolutionary theoryspecial relativity - to explain some of the most troubling problems in current physics concerning electromagnetism and motion. Soon afterward, Hermann Minkowski recast special relativity essentially as a new geometric structure for spacetime. These ideas are the subject of the first part of the book. The second part develops the main implications of Einstein's general relativity as a theory of gravity rooted in the differential geometry of surfaces.
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Product Details

  • ISBN-13: 9781441931429
  • Publisher: Springer New York
  • Publication date: 11/30/2013
  • Series: Undergraduate Texts in Mathematics Series
  • Edition description: Softcover reprint of hardcover 1st ed. 2000
  • Edition number: 1
  • Pages: 463
  • Sales rank: 1,531,313
  • Product dimensions: 6.69 (w) x 9.61 (h) x 0.97 (d)

Table of Contents

1 Relativity Before 1905 1
1.1 Spacetime 1
1.2 Galilean Transformations 9
1.3 The Michelson-Morley Experiment 15
1.4 Maxwell's Equations 22
2 Special Relativity - Kinematics 31
2.1 Einstein's Solution 31
2.2 Hyperbolic Functions 43
2.3 Minkowski Geometry 49
2.4 Physical Consequences 73
3 Special Relativity - Kinetics 87
3.1 Newton's Laws of Motion 87
3.2 Curves and Curvature 108
3.3 Accelerated Motion 123
4 Arbitrary Frames 143
4.1 Uniform Rotation 144
4.2 Linear Acceleration 155
4.3 Newtonian Gravity 167
4.4 Gravity in Special Relativity 188
5 Surfaces and Curvature 203
5.1 The Metric 203
5.2 Intrinsic Geometry on the Sphere 221
5.3 De Sitter Spacetime 230
5.4 Curvature of a Surface 241
6 Intrinsic Geometry 257
6.1 Theorema Egregium 257
6.2 Geodesics 268
6.3 Curved Spacetime 277
6.4 Mappings 292
6.5 Tensors 307
7 General Relativity 329
7.1 The Equations of Motion 330
7.2 The Vacuum Field Equations 344
7.3 The Matter Field Equations 366
8 Consequences 385
8.1 The Newtonian Approximation 386
8.2 Spherically Symmetric Fields 396
8.3 The Bending of Light 413
8.4 Perihelion Drift 421
Bibliography 435
Index 439
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