Suppose I have a Kerr black hole (rotating, uncharged) and I build a giant ring (a "Niven Ring") around it. I am interested in two related scenarios (I am confused about the second, but am also providing the first for completeness and in-case of my error):
- Ring lies in plane of black hole's rotation. Because frame dragging will "accelerate" a test particle from the perspective of a distant observer, I conjecture that frame dragging will "accelerate" the ring, making it match the rate of frame dragging (local observers perceive it to be at rest, however).
- Ring is spinning orthogonal to black hole's spin. This feels like the setup to a gyroscope problem, but I am hesitant to analyze it that way because frame dragging isn't (I think) a real force, but more a difference between reference frames (yes?).
What is the effect on the ring in this second scenario? In-particular, is there any gyroscopic precession that occurs?