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I have a GR exam on tuesday and getting a bit confused as to how to find the metric for an observer in free fall a distance two schwarzchild radii from a black hole.

I know this is a bit of a basic question but I am just wondering if I am correct to substitute r=2rs and dt=d(tau) into the usual metric and simplify. Also does this class as a radial trajectory so can you set d(theta) and d(phi) =0 ... HELP!!

Thanks :)