- #1

Haorong Wu

- 413

- 89

- TL;DR Summary
- Differentiation with respect to an affine parameter with an orthonormal tetrad.

Hi, there. I am doing differentiation with respect to an affine parameter ##s##, I am not sure whether my idea is right or wrong.

Let ##C## be a geodesic for light and the path length ##s## on it be the affine parameter. Now I need to calculate ##\frac {\partial f}{\partial s}##, with ##f## being some function. Meanwhile, I have constructed an orthonormal tetrad ##\{\mathbf e_\mu \}## along the geodesic ##C## where ##\mathbf e_3## is along the direction of the wave vector ##\mathbf k##.

I think since at every point, I have a tetrad and ##\mathbf e_3## is tangent to the geodesic, I could just calculate ##\frac {\partial f}{\partial s}=\frac {\partial f}{\partial x^3}##. Is this correct?

Thanks ahead.

Let ##C## be a geodesic for light and the path length ##s## on it be the affine parameter. Now I need to calculate ##\frac {\partial f}{\partial s}##, with ##f## being some function. Meanwhile, I have constructed an orthonormal tetrad ##\{\mathbf e_\mu \}## along the geodesic ##C## where ##\mathbf e_3## is along the direction of the wave vector ##\mathbf k##.

I think since at every point, I have a tetrad and ##\mathbf e_3## is tangent to the geodesic, I could just calculate ##\frac {\partial f}{\partial s}=\frac {\partial f}{\partial x^3}##. Is this correct?

Thanks ahead.