# Second order expansion of metric in free-fall

by InsertName
Tags: metric
 P: 27 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) + (dxidxj(δij - $\frac{1}{3}$ Rikjlxkxl) to second order. Does anyone know where I could find a derivation of this result?