Would infinite material cause a black hole?

Question

If you have an infinite amount of any material(That doesn't have a critical mass to have nuclear reactions), would this matter form massive black holes that condense into an infinite black hole? Two options I see: Either the gravitational pull from every molecule is identical, stretching infinitely in every direction, and thus there's no net force on the system, and so it never can cluster together to form black holes, or- Randomized motions of atoms cause the entire mass to shift enough that the atoms feel enough different strengths of forces of gravity that they are drawn together into a supermassive(literally infinite) black hole. What seems most likely: one of these two, or an entirely different result?

Answer 1

Your question touches upon two different issues.

If all the matter in the universe is precisely evenly distributed it can never collapse into denser structures because every particle in the universe feels a net zero force. However this is not physically reasonable. At any temperature above absolute zero there will be some random thermal motion, and this will cause density fluctuations.

Any fluctuation in density is unstable in the sense that if you make a region of the universe denser you increase its gravity. This attracts other matter towards the denser region and you get a vicious circle. So given that in any real universe fluctuations must exist, we expect that they will cause the initially nearly homogeneous universe to fragment into denser objects.

Whether black holes form depends on how quickly the matter can aggregate compared to the expansion of the universe. If the universe is expanding very rapidly then it will tend to pull matter apart faster than it can aggregate, and we will get only relatively small objects that won't form black holes. For a universe like ours the expansion is slow enough that objects like supermassive black holes can form. In fact they formed very early in the history of the universe.

So in general we do expect that black holes will be formed, and this addresses the first part of your question. The trouble is that you then ask:

the atoms feel enough different strengths of forces of gravity that they are drawn together into a supermassive(literally infinite) black hole

This obviously can't happen in an infinite universe because, well, it's infinite so you can never gather evertything in it into a single infinitely heavy black hole.

Aside from this rather obvious objection, the expansion of the universe places a limit on the maximum size of black holes. The supermassive black holes at the centre of galaxies will continue to grow because galaxies are still colliding - the Milky Way and the Andromeda galaxy will collide in a few billion years and their central black holes may well merge. However over very, very long timescales the expansion of the universe will pull the remaining galaxies too far apart for them to ever collide and their black holes will not grow (much) bigger.

There is a sense in which a single finite black hole could be formed, though not in our universe. Whether a universe expands or contracts depends on its average density. If the density is high enough an expanding universe will slow then start contracting again. The end point of the contraction is a singularity of infinite density$^1$. However this singularity is not a black hole - its spacetime geometry is different. It also isn't infinitely massive since closed universes are necessarily finite.

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$^1$ we expect that quantum gravity effects would prevent the density ever becoming infinite