gravity - Questions about the Jeans length

I have a couple of questions about the Jeans length. Suppose the universe has a homogeneous energy density, except there's a spherical region that is overdense.

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  I understand that if the region is smaller than the Jeans length, then pressure, which travels at the speed of sound (compared to the speed of gravity $c$), can build up fast enough to counteract the gravitational collapse. But if the region is bigger than the Jeans length, it collapses. What exactly does it mean? Does the region get smaller and smaller until it vanishes? Wouldn't this create a black hole, since you're stuffing all the energy of the overdense region into a smaller and smaller place?

  
  


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  Or, if the region is collapsing, wouldn't it eventually be smaller than the Jeans length, at which point it stops collapsing?

  
  
  


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  And what happens if the region is underdense, rather than overdense?