# Affine parameter along a geodesic

1. Jun 1, 2009

### emma83

Hello,

I have a general question concerning affine parameters along a geodesic.
I have an expression such as this:

$$exp(iU(r,\theta,\phi)/2) \sim 1 + iV(r,\theta,\phi)d\lambda/2$$

And the justification is: we obtain the infinitesimal value $$V$$ when we expand $$exp(iU(r,\theta,\phi)/2)$$ to $$O(d\lambda)$$

Now what does that mean ? Do I have to expand the left-hand side as power series in $$r,\theta,\phi$$? But then how do I recover $$d\lambda$$? Actually I don't understand how the variables from the spherical coordinates $$r,\theta,\phi$$ relate to the affine parameter $$\lambda$$ along the geodesic. Could someone explain me please how to proceed?