In what sense is ''Oppenheimer-Snyder collapse a time reversed closed FRW model" ?

That is, "Are closed FRW metric (k=1) and the geometry inside the collapsing homogeneous matter same?" If yes, how?

(FRW metric: $ds^2= -dt^2 + \frac{a^2(t)}{1-r^2}dr^2 + a^2r^2d\Omega^2$

OS metric: $ds^2= -e^\nu dt^2 + e^\lambda dr^2 + r^2d\Omega^2$

It would be nice, if some rigorous mathematical arguments are provided.)

Thanks in advance.

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  • 2
    $\begingroup$ Where is this quote from? What part of it in particular are unclear? $\endgroup$ – Communisty Jul 13 '17 at 11:29
  • $\begingroup$ The OS metric is an FRW geometry patched to a Schwarzschild geometry at the surface of the collapsing sphere. Can you make it clearer what exactly you are asking? $\endgroup$ – John Rennie Jul 13 '17 at 11:44
  • $\begingroup$ Yes, it's the closed metric and this gives all the details. $\endgroup$ – John Rennie Jul 13 '17 at 14:42
  • $\begingroup$ Exactly how does that give all the details? $\endgroup$ – Aarsh Chotalia Jul 13 '17 at 14:47

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