I'm asking about the case where an infalling object travels a path right through a rotating black hole, intact.
I want to provide a simple parallel for the purposes of question clarity:
A horse can take me from my house to a paddock, from Point a to Point b. Something then spooks the horse, a descending hot air balloon (for example) and it bolts far into the woods, going from Point b to Point c. While I'm unfamiliar with that section of the woods, the horse eventually calms down and I'm able to use a compass to return us both to my house. Going from Point c to Point a is journey I've never taken before. I can then go from Point a to Point b again if I wish.
Now, consider my approach to a rotating black hole from a space station, using a craft that produces thrust. At a suitable distance from the space station I disengage the thrust mechanism and allow the craft to drift from there, Point A, to the event horizon which I'm calling Point B (anywhere on the horizon). Presuming that the craft passes through any ringlike singularity and I'm not obliterated by infinite blue-shifting, I could emerge from the event horizon and travel far enough away so that I can regain control of the craft, a place I call Point C.
My question is, would I then be able to go from Point C to Point A?
Secondarily, would I be able to go from Point A to Point B again, refinding my original trajectory?
