I am trying to work out the theoretical limits on the size of a shell world (made with orbital rings constructed around a black hole). I have the following constraints:
- The light to the planet must be provided by a sun/suns (can't use artificial lighting)
- The day length should be about 24 hours, and there should be seasons with about the same time length as on earth.
- The sun/suns have to last for at least a billion years (it can't be much more massive than it is)
One limiting factor I have identified is that if the days are going to be created by the rotation of the planet, then when the planet gets larger, the velocity at the equator counteracts the force of gravity. I think that if gravity varied from 1/2 earth's at the equator to 2x earth's at the poles that would be ok though. Using this as the only limiting factor, I get that the maximum size is approximately 1000x earth size.
What other issues will there be for such a planet? Can a shell world even rotate that fast and not rip itself apart? What will the weather on such a planet be like? Will the sun be able to provide enough heat for a super massive planet?
Are there any other formulations that allow for a bigger system (using multiple suns/any other kind of 'natural' lighting system)?