I am writing a story where the main setting is a hollowed out asteroid with an interior biosphere and an exterior city. In this case, using centripetal force to simulate gravity would not work, because the biosphere is covering the entire interior surface, and the city is covering the exterior. I would like some ideas for creating a true artificial gravity field that would pull the people living on this asteroid towards its shell.
Couple answers here:
centripetal forces would still work, you spin the asteroid so that the interior is walkable (the poles wont be, but a good portion of the interior would). You build your cities on the exterior inverted so that floors are pointed toward space and ceilings toward the core.
Magical gravity field emitters placed across the surface that would exert a pull on the cities built on top of it and the biosphere built below it. -this would probably be the most realistic way to achieve this if we could actually harness gravity.
But if you are shopping for a scientifically grounded way of controlling the sub-atomic force known as gravity. We still know nothing more than adding mass.
If you imagine that we eventually succeed at a unified field theory, then we may be able to manipulate gravity as easily as we manipulate electromagnetism and electron flow. That hand waving argument would allow for pretty much any gravitational field strength and direction you desire within limits of energy supply and ability to afford the required equipment.
Our current understanding of physics does not have a mechanism for creating artificial gravity. Any science based explanation of this effect requires a science sufficiently advanced to be indistinguishable from magic.
Call the technology something cool and skip over the explanation for how they work.