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Alternate form of geodesic equation

  1. Aug 29, 2012 #1
    1. The problem statement, all variables and given/known data
    We're asked to show that the geodesic equation [tex]\frac{du^{a}}{dt} +\Gamma^{a}_{bc}u^{b}u^{c}=0[/tex] can be written in the form [tex]\frac{du_{a}}{dt}=\frac{1}{2}(\partial_{a}g_{cd})u^{c}u^{d}[/tex]




    2. Relevant equations
    [tex]\Gamma^{a}_{bc}=\frac{1}{2}g^{ad}(\partial_{b}g_{dc}+\partial_{c}g_{bd}-\partial_{d}g_{bc})[/tex]



    3. The attempt at a solution
    I tried contracting the geodesic equation with [tex]g_{ab}[/tex] but came out with some Kronecker deltas which stumped me a bit.
     
  2. jcsd
  3. Aug 29, 2012 #2
    It can't be true in general. (pun!)

    Is there some kind of simplifying assumption or approximation that makes 2 of the terms go away? Perhaps you're studying the Newtonian limit?
     
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