A rotating black hole is believed to contain a ring singularity rather than a point.
However, if an astronaut is orbiting the black hole at exactly the same angular velocity as the blackhole (in direction and magnitude), then it is no longer rotating to him.
Would it appear as a point singularity? (if he could somehow see it)
The ring singularity (assuming traditional GR is the whole story of gravity) is a definitive fact. It will remain a ring no matter what its observer does. This is in an absolutely identical sense to the objective difference between an inertial frame of reference (no pseudo-forces whatsoever) and a non-inertial frame (some kind of pseudo-forces).Tweet