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Geodesic Equation

  1. Aug 16, 2015 #1
    As the geodesic equation in a form of
    is quite familiar for me. But I still cannot derive it in terms of time coordinate parameter;
    I can't get the second term on the right hand side
    what I can get is

    How can I obtain that term?
  2. jcsd
  3. Aug 16, 2015 #2


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    I suggest you do not work in terms of the metric. The equation follows directly from the variable substitution to parameterise the curve with ##t## instead of ##s## and looking at how the geodesic equation transforms under this change. Keep in mind that
    \frac{d^2 t}{ds^2} = - \Gamma^0_{\alpha\beta} \dot x^\alpha \dot x^\beta .
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