Suppose we are given a Kerr spacetime (e.g. containing a single uncharged rotating black hole). How does one know that the coordinates chosen is rotating or non-rotating as seen from infinity? And how does one compute the angular velocity as seen by observer at infinity?
The standard choice of metric is written in Boyer-Lindquist coordinates: I presume this is a "asymptotically rotating coordinates". If coordinates are not an invariant concept, I should be able to, for instance, go into a "non-rotating" frame and write the metric differently. But I am confused as to how this can be done.