Creating a stable, liveable ringworld orbiting a binary black hole/stellar pair
I'm creating a setting for a sci-fi RPG. I would like to check whether the concept is physically possible. The main action happens on a giant ringworld which centrifugally orbits a paired black hole and star. Here is a diagram of what I mean:
I am hoping that this setup would provide a day-night cycle. When the star is visible from a point on the ringworld, it is "day". When the star goes "behind" the black hole, it becomes "night".
Constraints:
1. The ringworld orbit should be stable.
2. The star orbit around the black hole should be stable - ie the star is not feeding the black hole (due to radiation issues) and therefore there is no accretion disk.
3. The radius of the ringworld should be reasonable - between 0.1 - 2 AU.
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The mass of the star should be reasonable, erring on the smaller side
5. The mass of the black hole should be reasonable, erring on the smaller side
6. The irradiance (watts of radiation per square meter) on the ringworld should be comparable to that of Earth.
7. The wavelength profile of the irradiance on the ringworld should either: be comparable to that of Earth (preferable) or if the black hole generates insanely dangerous gamma rays (reduced due to no accretion disk?), it should be at least plausible that the ringworld has some sort of magnetic field generation technology powerful enough to deflect them.
8. The orbital period of the star around the back hole should be comparable to that of a day. Anywhere between 12-48 hours would work though.
9. Something also to consider: the day/night cycle will break down if the black hole Schwartzchild radius is smaller than the radius of the star. So the radius of the black hole has to be greater than the radius of the star. I imagine this will require a black hole of considerable mass. This can be scifi'd away with "inertial dampeners" in the ring or something if required.
Is such an orbital setup mathematically possible without leading to an absurdly large ring?
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