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Since a black hole radius is 2 times the mass, it seems like any infinite distribution of matter has to have voids of increasing size as the scale changes in order for the whole Universe not to collapse into a black hole.

Is this a possible reason why galactic voids exist?

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No, voids exist because they were formed BY gravitational collapses!

At the beginning, there was an uniform distribution of gas, with slight fluctuations of density here and there (small inhomogeneities). Then gravity collapsed the higher density regions, thus forming the voids around them and that we see today.

The higher density regions are now in the form of galaxies and clusters of galaxies.

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