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

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

by James J. Callahan
     
 

In 1905, Albert Einstein offered a revolutionary theory—special relativity—to explain some of the most troubling problems in current physics concerning electromagnetism and motion. Soon afterwards, 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.

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Overview

In 1905, Albert Einstein offered a revolutionary theory—special relativity—to explain some of the most troubling problems in current physics concerning electromagnetism and motion. Soon afterwards, 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. The author explores the way an individual observer views the world and how a pair of observers collaborate to gain objective knowledge of the world. To encompass both the general and special theory, he uses the geometry of spacetime as the unifying theme of the book. To read it, one needs only a first course in linear algebra and multivariable calculus and familiarity with the physical applications of calculus.

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
Pages:
463
Sales rank:
1,507,735
Product dimensions:
6.69(w) x 9.61(h) x 0.97(d)

Meet the Author

Table of Contents

Preface
1Relativity Before 19051
1.1Spacetime1
1.2Galilean Transformations9
1.3The Michelson-Morley Experiment15
1.4Maxwell's Equations22
2Special Relativity - Kinematics31
2.1Einstein's Solution31
2.2Hyperbolic Functions43
2.3Minkowski Geometry49
2.4Physical Consequences73
3Special Relativity - Kinetics87
3.1Newton's Laws of Motion87
3.2Curves and Curvature108
3.3Accelerated Motion123
4Arbitrary Frames143
4.1Uniform Rotation144
4.2Linear Acceleration155
4.3Newtonian Gravity167
4.4Gravity in Special Relativity188
5Surfaces and Curvature203
5.1The Metric203
5.2Intrinsic Geometry on the Sphere221
5.3De Sitter Spacetime230
5.4Curvature of a Surface241
6Intrinsic Geometry257
6.1Theorema Egregium257
6.2Geodesics268
6.3Curved Spacetime277
6.4Mappings292
6.5Tensors307
7General Relativity329
7.1The Equations of Motion330
7.2The Vacuum Field Equations344
7.3The Matter Field Equations366
8Consequences385
8.1The Newtonian Approximation386
8.2Spherically Symmetric Fields396
8.3The Bending of Light413
8.4Perihelion Drift421
Bibliography435
Index439

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