General Relativity

General Relativty is written in terms of tensor fields.

Coordinates and indices

First we define the variables:

Metric Tensor

(We should use matrix notation here(?))

Christoffel Symbols

Riemann Tensor

(Only the first two terms so far...[work in progress])

Geodesic Equation

Also need to write this with Id (matrix version) instead of g
We have a general problem of a function like \(x\Rightarrow y\Rightarrow \) and we want to curry either x or y first. Really we would like to write \(f(x,\_)\)
Alternative formulation using GL(4): $$\sqrt{1}$$