# 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.)

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

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