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General Relativity
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.
- Author
- Benjamin Crowell
- Publisher
- Fullerton College
- Source
- LibreTexts
- License
- CC BY-SA
- Language
- EN
- Category
- Basic Sciences
Contents· 91 sections
- 01: Geometric Theory of Spacetime
- 1.01: Time and Causality
- 1.02: Experimental Tests of the Nature of Time
- 1.03: Non-simultaneity and Maximum Speed of Cause and Effect
- 1.04: Ordered Geometry
- 1.05: The Equivalence Principle (Part 1)
- 1.06: The Equivalence Principle (Part 2)
- 1.E: Geometric Theory of Spacetime (Exercises)
- 02: Geometry of Flat Spacetime
- 2.01: Introduction to Geometry of Flat Spacetime
- 2.02: Affine Properties of Lorentz Geometry (Part 1)
- 2.03: Affine Properties of Lorentz Geometry (Part 2)
- 2.04: Relativistic Properties of Lorentz Geometry (Part 1)
- 2.05: Relativistic Properties of Lorentz Geometry (Part 2)
- 2.06: The Light Cone
- 2.07: Experimental Tests of Lorentz Geometry
- 2.08: Three Spatial Dimensions (Part 1)
- 2.09: Three Spatial Dimensions (Part 2)
- 2.E: Geometry of Flat Spacetime (Exercises)
- 03: Differential Geometry
- 3.01: Introduction to Differential Geometry
- 3.02: Tangent Vectors
- 3.03: Affine Notions and Parallel Transport
- 3.04: Models
- 3.05: Intrinsic Quantities
- 3.06: The Metric (Part 1)
- 3.07: The Metric (Part 2)
- 3.08: The Metric in General Relativity
- 3.09: Interpretation of Coordinate Independence
- 3.E: Differential Geometry (Exercises)
- 04: Tensors
- 4.01: Lorentz Scalars
- 4.02: Four-vectors (Part 1)
- 4.03: Four-vectors (Part 2)
- 4.04: The Tensor Transformation Laws
- 4.05: Experimental Tests
- 4.06: Conservation Laws
- 4.07: Things that Arent Quite Tensors
- 4.E: Tensors (Exercises)
- 05: Curvature
- 5.01: Introduction to Curvature
- 5.02: Tidal Curvature Versus Curvature Caused by Local Sources
- 5.03: The Stress-energy Tensor
- 5.04: Curvature in Two Spacelike Dimensions
- 5.05: Curvature Tensors
- 5.06: Some Order-of-magnitude Estimates
- 5.07: The Covariant Derivative
- 5.08: The Geodesic Equation
- 5.09: Torsion
- 5.10: From Metric to Curvature
- 5.11: Manifolds (Part 1)
- 5.12: Manifolds (Part 2)
- 5.13: Units in General Relativity
- 5.E: Curvature (Exercises)
- 06: Vacuum Solutions
- 6.01: Event Horizons
- 6.02: The Schwarzschild Metric (Part 1)
- 6.03: The Schwarzschild Metric (Part 2)
- 6.04: Black Holes (Part 1)
- 6.05: Black Holes (Part 2)
- 6.06: Degenerate Solutions
- 6.E: Vacuum Solutions (Exercises)
- 07: Symmetries
- 7.01: Killing Vectors
- 7.02: Spherical Symmetry
- 7.03: Penrose Diagrams and Causality
- 7.04: Static and Stationary Spacetimes (Part 1)
- 7.05: Static and Stationary Spacetimes (Part 2)
- 7.06: The Uniform Gravitational Field Revisited
- 7.E: Symmetries (Exercises)
- 08: Sources
- 8.01: Sources in General Relativity (Part 1)
- 8.02: Sources in General Relativity (Part 2)
- 8.03: Cosmological Solutions (Part I)
- 8.04: Cosmological Solutions (Part 2)
- 8.05: Cosmological Solutions (Part 3)
- 8.06: Sources in General Relativity (Part 3)
- 8.07: Cosmological Solutions (Part 4)
- 8.08: Mach's Principle Revisited
- 8.09: Historical Note - The Steady-state Model
- 8.E: Sources in General Relativity (Exercise)
- 09: Gravitational Waves
- 9.01: The Speed of Gravity
- 9.02: Gravitational Radiation (Part 1)
- 9.03: Gravitational Radiation (Part 2)
- 9.E: Gravitational Waves (Exercises)
- 10: Appendices
- 10.01: Appendix A (Part 1)
- 10.02: Appendix A (Part 2)
- 10.03: Appendix A (Part 3)
- 10.04: Appendix C