General Relativity

by Benjamin Crowell

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This is a textmap about general relativity, at a level that is meant to be accessible to advanced undergraduates. This is mainly a textmap about general relativity, not special relativity. For someone who has not already learned special relativity, I strongly recommend mastering it first.

Description from LibreTexts.

Publisher
Fullerton College
Subjects
Physics, Relativity
Licence
CC BY-SA 4.0, as LibreTexts states it
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: Geometric Theory of Spacetime
  7. 1.1: Time and Causality
  8. 1.2: Experimental Tests of the Nature of Time
  9. 1.3: Non-simultaneity and Maximum Speed of Cause and Effect
  10. 1.4: Ordered Geometry
  11. 1.5: The Equivalence Principle (Part 1)
  12. 1.6: The Equivalence Principle (Part 2)
  13. 1.E: Geometric Theory of Spacetime (Exercises)
  14. 2: Geometry of Flat Spacetime
  15. 2.1: Introduction to Geometry of Flat Spacetime
  16. 2.2: Affine Properties of Lorentz Geometry (Part 1)
  17. 2.3: Affine Properties of Lorentz Geometry (Part 2)
  18. 2.4: Relativistic Properties of Lorentz Geometry (Part 1)
  19. 2.5: Relativistic Properties of Lorentz Geometry (Part 2)
  20. 2.6: The Light Cone
  21. 2.7: Experimental Tests of Lorentz Geometry
  22. 2.8: Three Spatial Dimensions (Part 1)
  23. 2.9: Three Spatial Dimensions (Part 2)
  24. 2.E: Geometry of Flat Spacetime (Exercises)
  25. 3: Differential Geometry
  26. 3.1: Introduction to Differential Geometry
  27. 3.2: Tangent Vectors
  28. 3.3: Affine Notions and Parallel Transport
  29. 3.4: Models
  30. 3.5: Intrinsic Quantities
  31. 3.6: The Metric (Part 1)
  32. 3.7: The Metric (Part 2)
  33. 3.8: The Metric in General Relativity
  34. 3.9: Interpretation of Coordinate Independence
  35. 3.E: Differential Geometry (Exercises)
  36. 4: Tensors
  37. 4.1: Lorentz Scalars
  38. 4.2: Four-vectors (Part 1)
  39. 4.3: Four-vectors (Part 2)
  40. 4.4: The Tensor Transformation Laws
  41. 4.5: Experimental Tests
  42. 4.6: Conservation Laws
  43. 4.7: Things that Aren’t Quite Tensors
  44. 4.E: Tensors (Exercises)
  45. 5: Curvature
  46. 5.1: Introduction to Curvature
  47. 5.2: Tidal Curvature Versus Curvature Caused by Local Sources
  48. 5.3: The Stress-energy Tensor
  49. 5.4: Curvature in Two Spacelike Dimensions
  50. 5.5: Curvature Tensors
  51. 5.6: Some Order-of-magnitude Estimates
  52. 5.7: The Covariant Derivative
  53. 5.8: The Geodesic Equation
  54. 5.9: Torsion
  55. 5.10: From Metric to Curvature
  56. 5.11: Manifolds (Part 1)
  57. 5.12: Manifolds (Part 2)
  58. 5.13: Units in General Relativity
  59. 5.E: Curvature (Exercises)
  60. 6: Vacuum Solutions
  61. 6.1: Event Horizons
  62. 6.2: The Schwarzschild Metric (Part 1)
  63. 6.3: The Schwarzschild Metric (Part 2)
  64. 6.4: Black Holes (Part 1)
  65. 6.5: Black Holes (Part 2)
  66. 6.6: Degenerate Solutions
  67. 6.E: Vacuum Solutions (Exercises)
  68. 7: Symmetries
  69. 7.1: Killing Vectors
  70. 7.2: Spherical Symmetry
  71. 7.3: Penrose Diagrams and Causality
  72. 7.4: Static and Stationary Spacetimes (Part 1)
  73. 7.5: Static and Stationary Spacetimes (Part 2)
  74. 7.6: The Uniform Gravitational Field Revisited
  75. 7.E: Symmetries (Exercises)
  76. 8: Sources
  77. 8.1: Sources in General Relativity (Part 1)
  78. 8.2: Sources in General Relativity (Part 2)
  79. 8.3: Cosmological Solutions (Part I)
  80. 8.4: Cosmological Solutions (Part 2)
  81. 8.5: Cosmological Solutions (Part 3)
  82. 8.6: Sources in General Relativity (Part 3)
  83. 8.7: Cosmological Solutions (Part 4)
  84. 8.8: Mach's Principle Revisited
  85. 8.9: Historical Note - The Steady-state Model
  86. 8.E: Sources in General Relativity (Exercise)
  87. 9: Gravitational Waves
  88. 9.1: The Speed of Gravity
  89. 9.2: Gravitational Radiation (Part 1)
  90. 9.3: Gravitational Radiation (Part 2)
  91. 9.E: Gravitational Waves (Exercises)
  92. 10: Appendices
  93. 10.1: Appendix A (Part 1)
  94. 10.2: Appendix A (Part 2)
  95. 10.3: Appendix A (Part 3)
  96. 10.4: Appendix C
  97. Back Matter
  98. Index
  99. Index
  100. Glossary
  101. Detailed Licensing