Flowchart of subjects leading up to studying GR
The Lay of the Land (from different perspectives)
- Outline of Topics
- Overview
- Special Relativity
- The Equivalence Principle
- Coordinate systems and coordinate transformations
- Tensors and Invariant Equations
- Tensor Math
- Parallel Transport
- The Tensor Derivative
- The Schwarzschild solution
- The mathematical objects of interest
- – the Metric Tensor
- – The Christoffel (Connection) Symbol
- – The Riemann (Curvature) Tensor
- – The Ricci Tensor
- – The Ricci Scalar
- – The Energy-Momentum Tensor
- – The Einstein Tensor
- The Equations
- Einstein’s Equation:
- The Geodesic Equation:
- Coordinate Systems
- Boyer-Lindquist
- Eddington-Finkelstein
- Fermi normal
- Kerr-Schild
- Kruskal
- Painleve-Gullstrand
- Reimann normal
- Spacetimes
- de Sitter
- Friedmann-Robertson-Walker
- Kerr
- Kerr-Newman
- Majumdar-Papapetrou
- Minkowski
- Schwartschild
- Vaidya
- Horizons
- Apparent
- Cauchy
- Event
- Killing
- Trapping