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Yeah, I had already begun to worry about that second point, that the compressive pressure might be greater than I had imagined, but I couldn't see an easy way to calculate it. Your first point, that a black hole will form, is an easier way to see that this arrangement will fail. In fact I think the two points are different ways of looking at the same thing; for a black hole to form the shell must be pushed beyond the limit of its compressive strength.
What about a circular ring rather than a spherical shell? The mass is proportional to the radius, so it looks like it has a hope of working. But no, using the results of the paper here (behind a paywall, sorry) the pressure inside the ring rises with log(r), so it will eventually break.
:-(
Can we prove that all sufficiently large structures collapse?
Sketch of proof: you proved that a stick collapses (compression scaling as Log(L)).
Well every connected object is either a stick, a curvy stick, or one of those things plus some extra atoms. So - prove that making things curvy or adding atoms doesn't help (enough). So, e.g. thickening the stick in the middle won't save it since you'd need infinite thickness.
hmmm... we've been talking as if in a space without dark energy. But with dark energy, a sufficiently l... (read more)