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Lemaitre Coordinate from the E-F coordinate

  1. May 6, 2012 #1
    How can Eddington-Finkelstein coordinate be transformed into Lemaitre coordinate?

    I know the transformation between the Lemaitre and Schwarzschild coordinate, and also between Eddington-Finkelstein and Schwarzschild coordinate.

    So I tried to find the connection between Lemaitre and E-F coordinate from that, but it is very complicated..

    Can you give me the explicit formula for that?
     
  2. jcsd
  3. May 6, 2012 #2

    Mentz114

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    Gold Member

    If L1 takes LeMaitre basis to the Schwarzschild coordinate basis and L2 takes SS to E.F., then does L1L2 not take LeMaitre to EF basis ?

    Formally, if μ is the Schwarzschild coordinate index, a is a LeMaitre frame index and A is an EF frame index then
    [tex]
    \begin{align}
    v^\mu &= \Lambda^\mu_a v^a\\
    v^A &= \Lambda^A_\mu v^\mu = \Lambda^A_\mu(\Lambda^\mu_a v^a) = (\Lambda^A_\mu\Lambda^\mu_a)v^a
    \end{align}
    [/tex]
     
    Last edited: May 6, 2012
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