7. Christoffel Symbols

Kapitel in diesem Buch

1. Frontmatter i
2. Preface v
3. Contents vii
4. 1. Special relativity 1
5. 2. Oblique oxes 3
6. 3. Curvilinear coordinates 5
7. 4. Nontensors 8
8. 5. Curved Space 9
9. 6. Parallel Displacement 10
10. 7. Christoffel Symbols 12
11. 8. Geodesics 14
12. 9. The Stationary Property of Geodesics 16
13. 10. Covariant Differentiation 17
14. 11. The Curvature Tensor 20
15. 12. The Condition for Flat Space 22
16. 13. The Bianci Relations 23
17. 14. The Ricci Tensor 24
18. 15. Einstein’s Law of Gravitation 25
19. 16. The Newtonian Approximation 26
20. 17. The Gravitational Red Shift 29
21. 18. The Schwarzchild Solution 30
22. 19. Black Holes 32
23. 20. Tensor Densities 36
24. 21. Gauss and Stokes Theorems 38
25. 22. Harmonic Coordinates 40
26. 23. The Electromagnetic Field 41
27. 24. Modification of the Einstein Equations by the Presence of Matter 43
28. 25. The Material Energy Tensor 45
29. 26. The Gravitational Action Principle 48
30. 27. The Action for a Continuous Distribution of Matter 50
31. 28. The Action for the Electromagnetic Field 54
32. 29. The Action for Charged Matter 55
33. 30. The Comprehensive Action Principle 58
34. 31. The Pseudo-Energy Tensor of the Gravitational Field 61
35. 32. Explicit Expression for the Pseudo-Tensor 63
36. 33. Gravitational Waves 64
37. 34. The Polarization of Gravitational Waves 66
38. 35. The Cosmological Term 68
39. Index 71