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

ds^{2}= -c^{2}dt^{2}(1 + R_{0i0j}x^{i}x^{j}) - 2cdtdx^{i}([itex]\frac{2}{3}[/itex] R_{0jik}x^{j}x^{k}) + (dx^{i}dx^{j}(δ_{ij}- [itex]\frac{1}{3}[/itex] R_{ikjl}x^{k}x^{l})

to second order.

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

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# Second order expansion of metric in free-fall

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