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Affine parameter along a geodesic

  1. Jun 1, 2009 #1
    Hello,

    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?
     
  2. jcsd
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