Given the idea that gravity is always a factor (even though greater distances are excessively tiny), would everything eventually end up forming a single black hole?

My thinking is that, with infinite time, all mass will eventually be pulled together.

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    $\begingroup$ The universe is expanding though. $\endgroup$ – Ryan Thorngren Aug 24 '18 at 17:26
  • $\begingroup$ @RyanThorngren Does the expanding out-match the force of gravity, then? $\endgroup$ – David Starkey Aug 24 '18 at 17:43
  • $\begingroup$ Not only is the universe expanding it is expanding at an accelerating rate. $\endgroup$ – Lewis Miller Aug 24 '18 at 17:51
  • $\begingroup$ @LewisMiller So that would suggest that at some point, even black holes wouldn't have the energy to hold themselves together? Or is there an expected max speed for the expansion? $\endgroup$ – David Starkey Aug 24 '18 at 17:53
  • $\begingroup$ The expansion is still very small on the micro scale so gravitationally bound systems won't become unbound by the expansion. $\endgroup$ – Lewis Miller Aug 24 '18 at 17:57

My thinking is that, with infinite time, all mass will eventually be pulled together.

There are two competing factors here, gravitational attraction and universal expansion. Generally the later of the two is "more powerful" - from what we can see, the matter in the universe is too little and too spread out to have enough collective gravity to overcome the existing expansion. So at the universal level, no, we're not going to be one big black hole.

But that's at the macro level. At smaller scales there's huge variations in the spread of the matter, and there's areas in the universe where there is enough matter, and gravity, to overcome the expansion. So in the far future, the universe will be these little blobs of matter with huge amounts of space between them.

Now one example of a system who's gravity overcomes expansion is the Milky Way. So imagine the Milky Way far in the future, will everything be sucked into the black hole in the center?

Nope. Orbits still exist. The Earth has been floating around the Sun for a good 4.5 billion years now, and we're not in danger of falling in any time soon. That was not the case 4.5 + 0.5 billion years ago when what is today a nice clean Solar System was filled with junk. Back then things were crashing into each other all the time, and those collisions result in all sorts of random trajectories, some of which ended in the Sun. But after a while anything that wasn't roughly co-planar collided out and we're left with the Solar System we have today.

So if you roll that forward long enough, what you end up with is a universe full of black holes and other objects like neutron star cores, all orbiting their collective center of mass. These will be spread out a LOT from the other collections, much more empty than the universe today. Astronomy will be rather boring.

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    $\begingroup$ Orbiting bodies radiate gravitational waves, so everything eventually falls down and every galaxy should eventually become a black hole on steroids. It would take a very long time though, like a number of years with 50 to 100 zeroes. $\endgroup$ – safesphere Aug 24 '18 at 19:17
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    $\begingroup$ @safesphere: No, stars evaporate out of galaxies. $\endgroup$ – user4552 Aug 24 '18 at 21:04
  • $\begingroup$ @BenCrowell Great. How has this "escape plan" worked out so far for 4 million stars already eaten by $\text{Sagittarius A}^*$? $\endgroup$ – safesphere Aug 25 '18 at 8:11

Classically speaking, I think that all the universe will be involved in one black hole if in every point in the universe is satisfied the relation:

$ |\vec{G}\cdot \vec{u}| > |\vec{R}\cdot \vec{u}| $

where $ \vec{G} $ is the gravitational force generated by the black hole and $ \vec{R} $ is the result of every other forces that afflict the considered point and $\vec{u}$ unitary vector which direction is the line that joins the center of mass of the black hole and the point considered and verse is facing towards the center of mass of the black hole.

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