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Schwarzschild solution for Planetary Motion

  1. Dec 21, 2013 #1
    Schwarzschild solution for Planetary Motion:

    ##g_{ij}= \left( \begin{array}{cccc}
    \frac{1}{(1-(\frac{2*m}{r}))} & 0 & 0 & 0 \\
    0 & r^2 & 0 & 0 \\
    0 & 0 & r^2*(sin\theta)^2 & 0 \\
    0 & 0 & 0 & c^2*(1-\frac{2*m}{r})
    \end{array} \right)
    ##


    where ##m=\frac{G*(Mass of Sun)}{c^2}##

    My question is how do you find the Resultant Contravarient Position Vector.

    ##x^{'i} = \left( \begin{array}{c} r' \\ \theta' \\ \phi' \\ t' \end{array} \right)##
    given the Contravarient Position Vector.

    ##x^{i} = \left( \begin{array}{c} r \\ \theta \\ \phi \\ t \end{array} \right)##

    from the Schwarzschild Metric Tensor.
     
  2. jcsd
  3. Dec 21, 2013 #2

    Dale

    Staff: Mentor

    Last edited: Dec 21, 2013
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