Essential Relativity: Special, General, and Cosmological

Front Cover
Springer, Apr 17, 2013 - Science - 319 pages
This book is an attempt to bring the full range of relativity theory within reach of advanced undergraduates, while containing enough new material and simplifications of old arguments so as not to bore the expert teacher. Roughly equal coverage is given tospecial relativity, general relativity, and cosmology. With many judicious omissions it can be taught in one semester, but it would better serve as the basis of a year's work. It is my hope, anyway, that its level and style of presentation may appeal also to wider c1asses of readers unrestricted by credit considerations. General relativity, the modern theory of gravitation in which free particles move along "straightest possible" lines in curved spacetime, and cosmology, with its dynamics for the whole possibly curved uni verse, not only seem necessary for a scientist's balanced view of the world, but offer some of the greatest intellectual thrills of modern physics. Nevertheless, considered luxuries, they are usu ally squeezed out of the graduate curriculum by the pressure of specialization. Special relativity escapes this tag with a ven geance, and tends to be taught as a pure service discipline, with too little emphasis on its startling ideas. What better time, there fore, to enjoy these subjects for their own sake than as an und- v vi PREFACE graduate? In spite of its forbidding mathematical reputation, even general relativity is accessible at that stage.
 

Contents

Arguments for the Relativity Principle
12
Maxwellian Relativity
13
Origins of General Relativity
14
Machs Principle 16 Consequences of Machs Principle
15
Cosmology
18
Inertial and Gravitational Mass
20
The Equivalence Principle
22
The SemiStrong Equivalence Principle
25
Consequences of the Equivalence Principle
26
2
29
The Relativity of Simultaneity
35
4
40
6
41
Length Contraction
50
Velocity Transformation
59
BASIC IDEAS OF GENERAL RELATIVITY
65
EINSTEINIAN OPTICS
68
Static Fields Geodesics and Hamiltons Principle
71
9
74
15
131
16
132
18
136
20
152
FORMAL DEVELOPMENT OF GENERAL RELATIVITY
155
The Vacuum Field Equations of General Relativity
166
76
173
The Schwarzschild Radius
184
25
188
80
195
CHAPTER 9
211
83
221
84
227
86
237
Cosmic Dynamics According to PseudoNewtonian Theory
248
The Friedmann Models
257
Machs Principle Reexamined
271
INDEX
313
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