Relativity

Preface; Notation; Part I. Special Relativity: 1. Introduction: inertial systems and Galilei invariance of classical mechanics; 2. Light propagation in moving coordinate systems and Lorentz transformations; 3. Our world as a Minkowski space; 4. Mechanics of special relativity; 5. Optics of plane waves; 6. Four-dimensional vectors and tensors; 7. Electrodynamics in vacuo; 8. Transformation properties of electromagnetic fields: examples; 9. Null vectors and the algebraic properties of electromagnetic field tensors; 10. Charged point particles and their field; 11. Pole-dipole particles and their field; 12. Electrodynamics in media; 13. Perfect fluids and other physical theories; Part II. Riemannian Geometry: 14. Introduction: the force-free motion of particles in Newtonian mechanics; 15. Why Riemannian geometry?; 16. Riemannian space; 17. Tensor algebra; 18. The covariant derivative and parallel transport; 19. The curvature tensor; 20. Differential operators, integrals and integral laws; 21. Fundamental laws of physics in Riemannian spaces; Part III. Foundations of Einstein's Theory of Gravitation: 22. The fundamental equations of Einstein's theory of gravitation; 23. The Schwarzschild solution; 24. Experiments to verify the Schwarzschild metric; 25. Gravitational lenses; 26. The interior Schwarzschild solution; Part IV. Linearized Theory of Gravitation, Far Fields and Gravitational Waves: 27. The linearized Einstein theory of gravity; 28. Far fields due to arbitrary matter distributions and balance equations for momentum and angular momentum; 29. Gravitational waves; 30. The Cauchy problem for the Einstein field equations; Part V. Invariant Characterization of Exact Solutions: 31. Preferred vector fields and their properties; 32. The Petrov classification; 33. Killing vectors and groups of motion; 34. A survey of some selected classes of exact solutions; Part VI. Gravitational Collapse and Black Holes: 35. The Schwarzschild singularity; 36. Gravitational collapse - the possible life history of a spherically symmetric star; 37. Rotating black holes; 38. Black holes are not black - relativity theory and quantum theory; 39. The conformal structure of infinity; Part VII. Cosmology: 40. Robertson-Walker metrics and their properties; 41. The dynamics of Robertson-Walker metrics and the Friedmann universes; 42. Our Universe as a Friedmann model; 43. General cosmological models; Bibliography; Index.