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I don't understand this:

The more mass a Black Hole has, the more gravity it create! The more gravity it has, the more mass it can get!

With this lines, someday, all the universe will be a black hole.

Is this correct?

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No, it is not expected that all the matter in the universe will eventually be in the form of black holes. See… – Ben Crowell Sep 18 '13 at 22:51
It might be relevant to look at black hole thermodynamics (there's a WP article) and the generalized second law of thermodynamics. – Ben Crowell Sep 19 '13 at 15:44

Imagine how a black hole is formed. According to the most prevalent theory most black holes start out as supermassive stars - Much larger then our sun. As they run out of fuel to support their own weight they go through a series of implosions. The shock waves from those implosions throw off the outer shells of material into space while the core collapses into a black hole. A supernova.

As that material flies away in all directions it pushes everything in its path out with it, in many cases compressing the material it encounters enough to form new stars. Meanwhile the core has collapsed into a black hole, but its mass is less then that of the original star, its just compressed into a tiny region of space at the center of the supernova.

During the millions, and Billions of years that the star was burning it was eating up everything that came within its gravitational reach, and, presumably, had already absorbed most of the free floating material that was within its reach along its orbit.

When it collapsed and threw off its outer shells it created a bit of a vacuum, and since the black hole is less massive then the original star it really doesn't have much left within its gravitational reach. So it's going to sit there, mostly uneventfully, waiting for something to come its way. When that happens it will feed, and grow, and as it grows it might reach new material, perhaps those new stars that were formed by the casting off of its outer shells.

Eventually though it will have swallowed everything within its reach and settle down again, because those things outside its reach are more attracted to other things that have a stronger local pull on them. You would call that a state of equilibrium - and until something else travels too close to escape again, and extends its reach, again, it will sit there, mostly uneventfully, waiting for something to come it's way... again.

Meanwhile the universe is expanding at an ever increasing rate, leaving locally isolated patches of material to fend for themselves. Eventually that black hole may eat through much of that local material, even join with other black holes in the area, but if/when it does it will find itself alone, as all its neighbors are well beyond its reach, doing the same dance.

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First, you need at least 6-8 times the solar mass ($M_\odot$) to get a core-collapse supernova. Second, anything from that lower limit up until about 25$M_\odot$ makes a neutron star, not a black hole; you need greater than this to make a black hole. – Kyle Kanos Sep 19 '13 at 18:59
quite right, a hasty lookup with a bad result. It doesn't affect my answer very much so I think I will just generalize it to "much larger". – Jessie Boone Sep 19 '13 at 21:56

That conclusion does not (logically) follow from those two premises.

It's true that if a block hole gains mass, then it's gravitational pull on matter will be stronger. If the gravitational pull is stronger, then matter doesn't have to come as close to the black hole in order to be pulled in. It does not mean, however, than everything will be pulled in.

Someone will hopefully. speak about the expansion of the universe and argue it that way.

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Another point is that black holes can perhaps evaporate via Hawking radiation. – NowIGetToLearnWhatAHeadIs Sep 18 '13 at 22:15

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