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Math Help - Show the Lemaitre line element is equivilent to the Schwarzschild geometry

  1. #1
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    Show the Lemaitre line element is equivilent to the Schwarzschild geometry

    Hi I need to show that the Lematre Line element
    $<br />
ds^2 = c^2 dw^2 -\frac{4}{9} \left(\frac{9\mu}{2(z-cw)}\right)^{2/3} dz^2 - \left(\frac{9\mu}{2}(z-cw)^2\right)^{2/3} d \Omega^2<br />

    is equivilent to the Schwarzschild geometry i.e. has the line element
    $ <br />
ds^2 = c^2 \left(1-\frac{2\mu}{r}\right) dt^2 - \left(1-\frac{2\mu}{r}\right)^{-1} dr^2 - r^2 d\Omega^2<br />

    I'm thinking I essentially have to spot the coordinate transform used here and I've tried making the identification that
    $<br />
r^2 = \left(\frac{9\mu}{2}(z-cw)^2\right)^{2/3}<br />

    but it doesn't seem to be getting me anywhere, is there a quick way of doing this?
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  2. #2
    A Plied Mathematician
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    I can't say I'm an expert in relativity, but this page looked highly relevant.
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