Flowchart of subjects leading up to studying GR
Flowchart of calculations
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
- $latex g_{\mu\nu}$ – the Metric Tensor
- $latex \Gamma^{\mu}{}_{\alpha\beta}$ – The Christoffel (Connection) Symbol
- $latex R^{\alpha}{}_{\rho\gamma\beta}$ – The Riemann (Curvature) Tensor
- $latex R_{\mu\nu}$ – The Ricci Tensor
- $latex R$ – The Ricci Scalar
- $latex T$ – The Energy-Momentum Tensor
- $latex G_{\mu\nu}$ – The Einstein Tensor
- The Equations
- Einstein’s Equation: $latex R_{\mu\nu} – \frac{1}{2}Rg_{\mu\nu} = 8\pi GT_{\mu\nu}$
- The Geodesic Equation: $latex \frac{d^2x^{\mu}}{d\lambda^2} + \Gamma^{\mu}_{\rho\sigma}
\frac{dx^{\rho}}{d\lambda}\frac{dx^{\sigma}}{d\lambda} = 0$
- 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