General Relativity for Mathematicians
This is a book about physics, written for mathematicians. The readers we have in mind can be roughly described as those who: I. are mathematics graduate students with some knowledge of global differential geometry 2. have had the equivalent of freshman physics, and find popular accounts of astrophys...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1977, 1977
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| Edition: | 1st ed. 1977 |
| Series: | Graduate Texts in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 0 Preliminaries
- 0.0 Review and notation
- 0.1 Physics background
- 0.2 Preview of relativity
- 1 Spacetimes
- 1.0 Review and notation
- 1.1 Causal character
- 1.2 Time orientability
- 1.3 Spacetimes
- 1.4 Examples of spacetimes
- 2 Observers
- 2.0 Mathematical preliminaries
- 2.1 Observers and instantaneous observers
- 2.2 Gyroscope axes
- 2.3 Reference frames
- 3 Electromagnetism and matter
- One: Basic Concepts
- Two: Interactions
- Three: Other Matter Models
- 4 The Einstein field equation
- 4.0 Review and notation
- 4.1 The Einstein field equation
- 4.2 Ricci flat spacetimes
- 4.3 Gravitational attraction and the phenomenon of collapse
- 5 Photons
- 5.0 Mathematical preliminaries
- 5.1 Photons
- 5.2 Light signals
- 5.3 Synchronizable reference frames
- 5.4 Frequency ratio
- 5.5 Photon distribution functions
- 5.6 Integration on lightcones
- 5.7 A photon gas
- 6 Cosmology
- 6.0 Review, notation and mathematical preliminaries
- 6.1 Data
- 6.2 Cosmological models
- 6.3 The Einstein-de Sitter model
- 6.4 Simple cosmological models
- 6.5 The early universe
- 6.6 Other models
- 6.7 Appendix: Luminosity distance in the Einstein-de Sitter model
- 7 Further applications
- 7.0 Review and notation
- 7.1 Preview
- 7.2 Stationary spacetimes
- 7.3 The geometry of Schwarzschild spacetimes
- 7.4 The solar system
- 7.5 Black holes
- 7.6 Gravitational plane waves
- 8 Optional exercises: relativity
- 8.1 Lorentzian algebra
- 8.2 Differential topology and geometry
- 8.3 Chronology and causality
- 8.4 Isometries and characterizations of gravitational fields
- 8.5 The Einstein field equation
- 8.6 Gases
- 9 Optional exercises: Newtonian analogues
- 9.0 Review and notation
- 9.1 Maxwell’s equations
- 9.2 Particles
- 9.3 Gravity
- Glossary of symbols
- Index of basic notations