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

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

Physics

Comparison With Electromagnetic Waves

Cosmic Microwave Background

Cosmic microwave background.

More questions

• Do photons have energy?

• E and B modes w.r.t. polarization and their naming origin.

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