Interesting stuff!
I'd like to ask question that's probably based on false logic and thinking about it too hard would probably make one's head implode, but how would this work in the context of a rapidly rotating black hole, specifically in the ergosphere, which (if I understand correctly), is a region of spacetime that is rotating around the black hole at a velocity faster than the speed of light?
Specifically, let's imagine Anna, who is in a spaceship within the ergosphere, sending signals out in all directions. Let's assume her spaceship is immune to the tidal forces of the black hole (reasonable if the black hole is very large), and the ships engines are powerful enough to maintain its distance from the center of the hole (also reasonable as it's outside the event horizon, but the ship cannot maintain a *fixed* position and thus must orbit the hole).
Let's say there is an observer, Bob, who is far away from the hole and maintains a fixed position relative to it. Bob is monitoring Anna's signals.
Now I have a lot of difficulty trying to visualize this, but doesn't the "FTL" velocity of the ergosphere mean that some of Anna's signals would be essentially travelling backward in time relative to Bob (from some reference frames)? At the very least I imagine some funky time-dilation effects would be seen but I'm just not sure what they would be like. If anyone can better analyze this scenario, feedback would be greatly appreciated.
