Gravity Wave
Make analogies of what you don’t know to what you know.
Questions

What is a gravity wave?

How can we observe gravity waves?

Why is it important?
Basic Math Tools
Covariance and contravariance of vectors
I found a series of Khan lectures on the maths related to Einstein notation. I should go through the basics before doing anything special, cuz you can only speak after you learn the language.
There is a simple example for superscript and subscript. A simple rule is that subscripts represent row vectors and superscripts represent column vectors. (This is ONLY true for Euclidean space.)
A Complete Guide to The Ricci Tensor.
Riemann geometry
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Take a look at electromagnetic tensor. The Maxwell’s equations can be derived from from the Lagrangian formulation.
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Degree of freedom:
 symmetry of 3x3 tensor –> 6
 traceless: \( g_{ii} = 0 \) –> 5
Dimensional Analysis
Physics
Comparison With Electromagnetic Waves
Cosmic Microwave Background
More questions

Scalar, vector, and tensor modes in gravitational waves? Here is a related paper of simulations.