Aside from what they did in that book, real generation ships will not be hollowed out asteroids!!! They’ll be built of the lightest materials possible (carbon fiber?) and encased in clean water ice for shielding and propellant… A generation ship will probably be shaped like a ring rotating around an engine cylinder. Inside the ring, the living sections will be able to swivel so that they experience 1G acceleration as gravity, and then switch to spinning while stationary or coasting between stars. See “The Jupiter Theft”.
This video demonstrates a ship which uses the concept to reconfigure it’s artificial gravity system from using centripetal force to using acceleration, on the fly, as the engines fire. However, I would dispense with much of the heavy rigid structure and simply attach the habitat modules to the thruster using cables: https://www.youtube.com/watch?v=jog1w_vOSQI
Stationary colonies however, will be heavier. Made out of asteroid rock, but not made of hollowed asteroids. Asteroids are loose piles of rubble, uneven density throughout. You need something strong enough that it can be a mile across, and be spun on it’s long axis for simulated gravity. So, the powdered tailings from mining will be sintered (melted and sprayed in place) into cylinders, appearing much like a concrete or ceramic material.
