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Re-parametrization of geodesics

  1. Oct 30, 2012 #1

    If I find a solution of the geodesic equation and I change the parametrization, the new function does not
    satisfy this equation for a general re-parametrization. But the world line is the same.

    Can you confirm it: does it come from the fact that we usually choose [itex]\nabla_VV=0[/itex] instead of
    [itex]\nabla_VV=fV[/itex]for the geodesic equation?
  2. jcsd
  3. Oct 30, 2012 #2


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    Yes. Only parameters related by a linear function will satisfy the simple form of geodesic equation. Further, invariant interval (proper time or distance) is one of the possible solutions, so only e.g. aτ+b will work as another parametrization and still satisfy this equation.
  4. Oct 30, 2012 #3
    Ok, thank you.
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