A Volunteer Program

Chapter 1 (Introduction)

1. Basic elements and preparation.
2. Introduction to Galilean Relativity
3. Introduction to Special relativity
4. Introduction to General Relativity

Chapter 2 (Preparation)

1. Covariant and Contravariant
2. Graphs and Diagrams
3. Speed of Light

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Chapter 3 (Galilean Relativity)

1. Galilean principle of Relative motions
2. Galilean Spacetime separation
3. Introduction to Invariants
4. Galilean Transformation
5. Euclidean Metric Tensor
6. Incompatibilities of Galilean Relativity

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Chapter 4 (Special Relativity)

1. Lorentz Transformation
2. Time Dilation
3. Length Contraction
4. Velocity addition
5. Relativity of simultaneity
6. Minkowski Metric
7. 4-Vectors

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Chapter 5 (Acceleration in Special Relativity)

1. Rindler Coordinates and Rindler Metric
2. Bell’s Spaceship Paradox
3. The Jacobian
4. Twin Paradox
5. Proper Time along curves
6. Covariant derivatives in flat Spacetime
7. Geodesics and Curved light beams

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Chapter 6 (Tensors)

1. Introduction to Tensors
2. Frequency waves
3. Covectors
4. Doppler shift with accelerating frames
5. Introduction to Metric Tensor
6. Introduction to Einstein’s Tensor

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Chapter 7 (General Relativity)

1. General Relativity basics
2. Equivalence principle
3. Proper acceleration
4. Manifolds
5. Covariant derivatives and Geodesics
6. Curvature
   1. Riemann Tensor
   2. Ricci Tensor
   3. Ricci Scalar
7. Newton Cartan Theory
8. Stress Energy Momentum Tensor
9. Einstein’s Field Equations Derivations

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Chapter 8 (Significances of General Relativity)

1. Schwarzschild Metric
2. Gravitational Time Dilation
3. Event Horizon
4. Eddington-Finkelstein
5. Kruskal-Szekeres
6. White/Wormholes

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Chapter 9 (Gravitational Waves)

1. Intro to LIGO
2. Linearized Gravity
3. GW Derivation
4. Transverse-Traceless Gauge
5. G Waves and Free Particles
6. Introduction to Modern Cosmology
7. FLRW Metric derivation
8. Cosmic Rest Frame