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After all, the density of matter in the first fraction of a second was much higher than that found in any star, and dense matter is supposed to curve spacetime strongly. At sufficient density there must be matter contained within a region smaller than the Schwarzschild radius for its mass. Was the force of the big bang stronger that the gravitational push?

Where did this infinitely dense matter originate from before the big bang? Was the big bang its self already a black hole and simply spewing matter at the end of it's life?

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Just after the big bang, the Universe was well approximated by a Friedman Robertson Walker metric which implies an infinite spatial extent and uniform density. A black hole forms when you have a collapsed object in less dense region.

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