Author | Sachs, Rainer K. author |
---|---|
Title | General Relativity for Mathematicians [electronic resource] / by Rainer K. Sachs, Hung-Hsi Wu |
Imprint | New York, NY : Springer New York, 1977 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-9903-5 |
Descript | XII, 292 p. online resource |
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 Maxwellโs equations -- 9.2 Particles -- 9.3 Gravity -- Glossary of symbols -- Index of basic notations