This book's principal aim is to clarify fundamental concepts, decipher mathematical structures used to model space-time and relativistic worlds, and to disclose their physical meaning. After each chapter, philosophical implications of the presented material are commented upon. Both special and general theories of relativity are presented in the book with the stress on their global aspects. Although global mathematical methods are extensively used throughout the book the definitions of new concepts, short comments and examples aim to make reading smooth without consulting other textbooks or review papers.
Author(s): Michael Heller
Publisher: World Scientific Pub Co Inc
Year: 1992
Language: English
Pages: C, viii, 147, B
Preface
Chapter 1 Manifold Model of Space-Time
0. Introduction
1. Banach Spaces and Manifolds- Mathematical Environment of the Space-Time Theory
£. Differential Manifolds
3. Orientability of Manifolds
. { Vector and Tensor Fields on Manifolds
5. Submanifolds
6. Manifold as a Model of Space-Time
7. Comments and Remarks
Chapter 2 Relativistic Model of Space-Time
0. Introduction
1. Metric Manifolds
2. Metric Model of Space-Time
9. Space-Time of Special Relativity
4. The Existence of the Lorentz Structure
5. Comments and Remarks
Chapter 3 Method of Fibre Bundles
0. Introduction
1. Fibre Bundles
!J. Principal and Associated Fibre Bundles
3. Connections in a Principal Fibre Bundle
4. Geometry of Principal Fibre Bundles
5. Geometry of the Frame Bundle
6. Applications to Gauge Theories
Chapter 4 The Frame Bundle and General Relativity
0. Introduction
1. Geometry of the Frame Bundle (continuation}
2. Geometry of the Base Manifold
9. Geometry of the Base Manifold (continuation}
4. The Fibre Bundle of Orthonormal Frames
5. General Relativity
6. Comments and Remarks
Chapter 5 The Cosmological Problem
0. Introduction
1. Cosmology as a Global Geometry of Space-Time
2. Cosmology as a Theory of the Ensemble of Universes
9. Observational Problems of Cosmology
Chapter 6 Geometry of the Standard Cosmological Model
0. Introduction
1. Warped Products
2. Macroscopic Description of Particles and Observers
9. Construction of the Standard Cosmological Model
4. Evolution of the Standard Cosmological Model.
5. Dust Filled and Radiation Filled Universes
6. Observational Background of the Standard Cosmological Model
7. Comments and Remarks
Bibliographical Essay
A. Classical Period (from the origin of relativistic cosmology to the Second World War).
B. Period of Stagnation (from the Second World War to the discovery of the background radiation in 1965}.
C. Period of Dynamical Progress (after the discovery of the background radiation).
Appendix Evolution of Dynamical Space-Time Theories
0. Introduction
1. Elementary Repetition of the Category Theory
2. Aristotelian Space-Time
3. Space-Time of Classical Mechanics Without Gravitational Field
..f. Space-Time of Classical Mechanics with Gravitational Field
5. The Special and General Theories of Relativity
References
Symbol Index
Author and Subject Index
Back Cover
