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Schwarzschild metric

  1. Apr 21, 2005 #1
    Light rays in the schwarzschild metric satisfy the differential equation


    \frac {d^2u} {d\phi^2}+u=3Mu^2



    I want to show that there is closed orbits with constant radius and also calculate the radius of the orbits as a function of the Schwarzchild radius.
    Can anyone help me with this? Or give me some hits?
    As simple as possible plz.
  2. jcsd
  3. Apr 21, 2005 #2


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    Staff Emeritus
    Science Advisor

    Well, if the orbit is one of constant radius, then du/dphi must be equal to zero, and so must du^2/dphi^2.

    You are then left with the equation u = 3Mu^2. Solve for u.
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