The standard science-fiction model, the received wisdom shared across hundreds of short stories and novels, is that people living in the asteroid belt will hollow out rocks with nuclear bombs or X-ray lasers and spin them up so centrifugal force will provide an analog of gravity to hold stuff to the inner surface. Pump in an atmosphere, garden the interior, knock out a few windows, or kindle a fusion tube hung in the zero gravity of the spin axis, and you have a cosy home.
The problem with this old trope (apart from the minor inconvenience of having every stone and boulder on the surface of your asteroid flying off when you spin it up to a rate that would provide useful gravity), is that most asteroids don't appear to be solid monolithic bodies suitable for that kind of engineering. Most seem to be lumpy piles of rock and dust, the larger ones held together by gravity and friction, the smaller ones held together by Van Der Waals forces (which explains why some smaller asteroids are rotating at speeds that should cause them to break up). That most asteroids are rubble piles would explain why none larger than 200 metres across rotate faster than once every 2.2 hours; above that speed limit, rock piles would disintegrate. Some smaller asteroids do spin faster than that, and are presumably solid all the way through, but if you hollowed them out they wouldn't provide much living space - although they would make nifty little spacecraft. So unless you're prepared to melt an entire asteroid, to fuse it into a solid body, you'll have to come up with another solution.
Given all that, when I was writing Evening's Empires, largely set in the asteroid belt, I had to come up with a few alternatives to the old hollow-asteroid model. Tunnelling labyrinths through the impacted rinds of rock piles. Coring small asteroids down their spin axes, providing living space equivalent to a skyscraper a kilometre or more tall. Tenting over craters to create cities and gardens - there are plenty of craters on asteroids. Tenting an entire rock, gardening the surface with parklands, forests and wildernesses, and hanging cities from the ceiling (you'd have to have pretty good defence systems to take down anything liable to impact with your soap-bubble world, but let's posit that in a couple or three centuries every fragment of rock more than a metre in diameter has been mapped, and pebbles and dust have been cleared from the orbits of inhabited asteroids by robot scoopships). Or intercepting comets, and use the CHON stuff to spin bubble habitats of every size from tough fullerenes and diamond composites. Those are just a few ideas. I leave it as an exercise to the reader to come up with others.
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