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I have a general question concerning affine parameters along a geodesic.

I have an expression such as this:

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

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

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

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# Affine parameter along a geodesic

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