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I know that the net curvature of the universe is zero due to the positive mass and the dark matter. But we say that a black hole creates infinite curvature in space-time. So, there must be a negative infinite curvature or else, the universe is no more flat. Where is the negative curvature formed?

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  • $\begingroup$ As far as I know, we are not yet certain if the universe has K =0, although the current density of the universe is observed to be very close to this critical value. Also we can only see part of the universe.en.m.wikipedia.org/wiki/Flatness_problem $\endgroup$ – user108787 Aug 3 '16 at 16:06
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    $\begingroup$ Your question is touching the relation between de Sitter and Schwarzschild metric. The answer to this question might provide you with some hints. $\endgroup$ – Moonraker Aug 3 '16 at 17:31
  • $\begingroup$ @count_to_10 has it right, if you "know" all these things, then you "know" more than all of us combined. All we know is that the hypothesis that the observable universe is flat can not be ruled out with the existing data. That doesn't mean anything for the universe in totality. It could be a giant pretzel for all we know. $\endgroup$ – CuriousOne Aug 3 '16 at 19:34
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By universe I assume you mean the observable universe, and yes indeed the curvature observed is close to zero, theorized to be due to the early universe inflation which flattened it in our observable spacetime.

The infinite curvature of a black hole (BH) is the singularity theorized to be inside the horizon. When you are outside, which we all are, it just seems like a mass of a certain amount. There are billions of BHs estimated to be in the observable universe and a bunch (not a billion or million) have been detected, basically the ones that are supermassive at the center of most galaxies, and some of which emit a huge amount of EM radiation as the accretion disk matter falls into the BH, basically the quasars.

The sum total of those BHs are a small percentage of the mass of the universe, and have no significant enough matter density, in cosmological terms, to affect the curvature of spacetime. As said before, their singularities (whether real or not, no matter) inside the BHs do not affect us, we only sense their gravitational mass. It is also thought with some good numerical and observational arguments that there is not very likely enough BHs that would have been created during and soon after the Big Bang to have them account for the dark matter density in the universe. Their gravitational radiation would certainly not have been enough to do much, just like the Big Bang gravitational radiation (which is expected to be detectable with space based interferometers) also would not be enough to do much to the overall curvature.

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