Make analogies of what you don’t know to what you know.


  • What is a gravity wave?

  • How can we observe gravity waves?

  • Why is it important?

Basic Math Tools

Einstein notation

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


Take a look at electromagnetic tensor. The Maxwell’s equations can be derived from from the Lagrangian formulation.


Degree of freedom:

  • symmetry of 3x3 tensor –> 6
  • traceless: \( g_{ii} = 0 \) –> 5

Dimensional Analysis


Comparison With Electromagnetic Waves

Cosmic Microwave Background

Cosmic microwave background.

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