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?


You can only recover conformally related spacetimes from its null geodesics, that is, the class of spacetimes related by the transformation

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

which possess a different matter content

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    $\begingroup$ This is interesting. Is there a good source where I can read more? $\endgroup$ – JohnnyMo1 Jul 28 '15 at 20:23
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    $\begingroup$ Check Hawking/Ellis pp.60--61 and Wald, p.445. Cheers. $\endgroup$ – Ivica Smolić Jul 28 '15 at 21:54

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