A Note on Indices in General Relativity

Virtually every equation in general relativity contains many indices, for example:

x`^μ= M^μ_νx^ν.

It is important to keep these indices straight as you are working!

There are “streamlined” notations sometimes used where instead one simply writes x`=Mx, which is great when you are writing. Unfortunately when you try to make a calculation with this notation, you end up having to spend time working out what the equation actually is telling you to do, which usually involves writing out the equation again with all the indices included.