Theoretical Foundations of Cosmology: Introduction to the Global Structure of Space-Time

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Outlines the assumptions on which relativistic cosmology is based, using the methods of global mathematics, clarifying concepts and showing the efficiency of structures to readers familiar with the mathematical calculations. Acidic paper. Annotation c. Book News, Inc., Portland, OR (
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Product Details

  • ISBN-13: 9789810207564
  • Publisher: World Scientific Publishing Company, Incorporated
  • Publication date: 4/28/1992
  • Pages: 160

Table of Contents

Ch. 1 Manifold Model of Space-Time 1
1 Banach Spaces and Manifolds--Mathematical Environment of the Space-Time Theory 2
2 Differential Manifolds 5
3 Orientability of Manifolds 10
4 Vector and Tensor Fields on Manifolds 11
5 Submanifolds 14
6 Manifold as a Model of Space-Time 15
7 Comments and Remarks 16
Bibliographical Note 19
Ch. 2 Relativistic Model of Space-Time 21
1 Metric Manifolds 22
2 Metric Model of Space-Time 24
3 Space-Time of Special Relativity 25
4 The Existence of the Lorentz Structure 27
5 Comments and Remarks 30
Bibliographical Note 32
Ch. 3 Method of Fibre Bundles 34
1 Fibre Bundles 36
2 Principal and Associated Fibre Bundles 39
3 Connections in a Principal Fibre Bundle 41
4 Geometry of Principal Fibre Bundles 45
5 Geometry of the Frame Bundle 47
6 Applications to Gauge Theories 49
Bibliographical Note 51
Ch. 4 The Frame Bundle and General Relativity 52
1 Geometry of the Frame Bundle (continuation) 53
2 Geometry of the Base Manifold 56
3 Geometry of the Base Manifold (continuation) 58
4 The Fibre Bundle of Orthonormal Frames 59
5 General Relativity 61
6 Comments and Remarks 63
Bibliographical Note 65
Ch. 5 The Cosmological Problem 66
1 Cosmology as a Global Geometry of Space-Time 67
2 Cosmology as a Theory of the Ensemble of Universes 70
3 Observational Problems of Cosmology 76
Ch. 6 Geometry of the Standard Cosmological Model 83
1 Warped Products 84
2 Macroscopic Description of Particles and Observers 86
3 Construction of the Standard Cosmological Model 88
4 Evolution of the Standard Cosmological Model 90
5 Dust Filled and Radiation Filled Universes 93
6 Observational Background of the Standard Cosmological Model 94
7 Comments and Remarks 101
Bibliographical Essay 106
Appendix. Evolution of Dynamical Space-Time Theories 112
1 Elementary Repetition of the Category Theory 113
2 Aristotelian Space-Time 117
3 Space-Time of Classical Mechanics Without Gravitational Field 118
4 Space-Time of Classical Mechanics with Gravitational Field 121
5 The Special and General Theories of Relativity 122
6 Comments and Remarks 122
Bibliographical Note 125
References 126
Symbol Index 135
Author and Subject Index 141
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