- #1

Pacopag

- 197

- 4

## Homework Statement

I would like to manipulate the geodesic equation.

## Homework Equations

The geodesic equation is usually written as

[tex]k^{a}{}_{;b} k^{b}=\kappa k^{a}[/tex] (it is important for my purpose to keep it in non-affine form).

It is clear that by contracting with the metric we may write alternatively

[tex]k_{a ;b} k^{b} = \kappa k_{a}[/tex].

What I would like to know is how to raise to a contravariant indices in the derivative on the left-hand side.

## The Attempt at a Solution

If I had to guess, I would like to be able to write something like.

[tex]k^{a ;b} k_{b}=\kappa k^{a}[/tex].

Is this a valid form of the geodesic equation?