# Thread: Show the Lemaitre line element is equivilent to the Schwarzschild geometry

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

Hi I need to show that the Lematre Line element
$\displaystyle$
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
$is equivilent to the Schwarzschild geometry i.e. has the line element$\displaystyle $ds^2 = c^2 \left(1-\frac{2\mu}{r}\right) dt^2 - \left(1-\frac{2\mu}{r}\right)^{-1} dr^2 - r^2 d\Omega^2$

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

but it doesn't seem to be getting me anywhere, is there a quick way of doing this?

2. I can't say I'm an expert in relativity, but this page looked highly relevant.