Black Hole Ringworld

Completed 2018-11-13. Available releases:
Imagine a ringworld built around a star. After eons of bliss, the star dies. Through the use of advanced technology, the ringworld itself survives intact, but the black hole remaining casts little light. In that late universe, the only remaining stars would be red dwarfs, so our advanced but dying civilization might move one (e.g. using a Shkadov thruster) to orbit the black hole itself, giving a hundred billion years of twilight.
This is what it would look like. Although I initially tried sketching out what I thought it looks like, I didn't feel confident in my intuition to give me an accurate result. Therefore, I wrote a raymarcher and had my computer do the heavy lifting. It turns out I actually got it mostly right, but the ease with which I could make modifications led me to change the viewpoint to this, much-more-cinematic, perspective. I then sketched that out in a quick colored-pencil drawing, producing this.
The black hole is a Kerr black hole (as most are), meaning it spins around its axis. You're looking down that axis, with the ringworld circling above and below. The red dwarf is orbiting very close to the event horizon and is being torn apart by tidal forces. You can see two main images of it, magnified (these also produce two faint lens flares, which you may be able to pick out). The black hole's frame-dragging and gravitational lensing twists the image of the ring around into a confusing shape and also Doppler-shifts it—the upper limb is bluer and the lower is redder.
Realism-wise, the black hole is probably much too large and therefore the effect far too dramatic. Also, although the geometry was calculated by a computer, and the light ray paths should be roughly correct, the relative distortion contribution of the spin vs. gravity, as well as the color, may be physically impossible (or not). Also, the system is gravitationally unstable (but ringworlds alone are gravitationally unstable and you weren't complaining about that).
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