# Would people living on different ringworlds around the same star measure time differently?

Okay so I have a sci-fi world masquerading as a fantasy world where numerous different genetically-engineered humanoids live on nine different ringworlds orbiting an artificial Earth-mass black hole (which they see as a "black sun"). The black hole's accretion disk provides light to the ringworlds much like a small star would, but if we take it as a given that these rings all revolve around the black hole at various rotational speeds (like the planets in our solar system do relative to the sun), how would the cultures living on these ringworlds measure time differently? Assuming of course that one ring passing into the shadow created by the ring above or below it (depending on which side of the ring you're living) is analogous to a single night.

EDIT: Hmmm... actually you're probably right. I want this whole structure to be Earth-sized so traveling across all the different rings doesn't take much longer than an IRL cross-continental journey apiece, but I also want the black hole to be small enough that the rings don't fall in. Anyone have any suggestions as to what would be an appropriate size that'd balance luminosity and gravity for a planet-sized structure?

As for the shape and arrangement of the structure it's similar in concept to the Game of Thrones opening:

https://i.stack.imgur.com/pqf90.jpg

• Please describe the attitude of the rings. Are these concentric Niven ringworlds, or Halos? I'm not sure of your day/night description.
– Ross
Sep 8, 2016 at 20:48
• I'm having difficulty envisioning what you are describing. Are the rings centered on the blackhole, or smaller objects orbiting the black hole. Sep 8, 2016 at 20:49
• If the ringworlds lie on the same plane the outer rings wouldn't get any light from the accretion disk (it would be shadowed by the first ringworld). You need space mirrors to get them light, if they don't lie on the smae plane things get complicated. The rings are not "in orbit" so you can rotate at the speed you want! You can even have the same timekeeping on all rings (but gravity would be different!) Sep 8, 2016 at 20:50
• Oh I see! When you say ringworld people think about Niven ring. In this case I think you are talking about a Bank's Orbital, they are VERY different things! Sep 8, 2016 at 20:55
• One wonders why make the "sun" so small, and where the inhabitants will get their heat, as I don't expect a tiny little black hole's disc of falling matter to be that warm or bright. (maybe in the x-ray range) Sep 8, 2016 at 21:13