## Second order expansion of metric in free-fall

Hello,

I have read that, in a freely-falling frame, the metric/ interval will be of the form:

ds2 = -c2dt2(1 + R0i0jxixj) - 2cdtdxi($\frac{2}{3}$ R0jikxjxk) + (dxidxjij - $\frac{1}{3}$ Rikjlxkxl)

to second order.

Does anyone know where I could find a derivation of this result?
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