# Can you recover a spacetime from its null geodesics?

So, I know that you can learn a lot about a spacetime from its causal structure, but can one completely recover the metric of a spacetime, just knowing the equations for the null geodesics in it?

If so, how would one go about doing this?

$g_{\mu\nu} \rightarrow \Omega^2(x) g_{\mu\nu}$