So, the canned explanation that I always hear about why the white hole solution of the extended Schwarzschild solution is non-physical is that "The matter distribution cuts off the white hole solution."
If I look at Oppenheimer-Snyder collapse, however, the cosmological solution that I paste to in the dust's interior is just the closed pressureless model of the Robertson-Walker metric, which is perfectly time-symmetric about the point of maximal expansion. If I look at this naïvely, then, the fluid in the Oppenheimer-Snyder solution originated in a singularity, which then disintegrates, to form an expanded fluid, which reaches some maximal extent, and then recollapses to form a singularity in the future, after some finite time. That past singularity sure seems like a white hole to me.
What am I misinterpreting here? Or is it just a pathology of the Oppenheimer-Snyder construction that it is over-simple, and more physically realistic matter models WOULD cut off the past singularity?