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Integral of geodesic equations

  1. Apr 9, 2014 #1
    Kevin Brown, in his excellent book "Reflections on Relativity" p. 409, "immediately" integrates 2 geodesic equations:



    to get:



    Does anyone understand that? I certainly don't.
  2. jcsd
  3. Apr 9, 2014 #2


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    They both go pretty much the same way. For the second one,

    [tex]\begin{eqnarray*}\frac{\frac{d^2 \phi}{ds^2}}{\frac{d \phi}{ds}} &=& - \frac{2}{r}\frac{dr}{ds}\\
    \frac{d}{ds}(\ln(\frac{d \phi}{ds})) &=& -2 \frac{d}{ds} \ln(r)\\
    \ln(\frac{d \phi}{ds}) &=& -2 \ln(r) + const\\
    \frac{d \phi}{ds} &=& \frac{h}{r^2}\end{eqnarray*}[/tex]
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