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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.

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  • $\begingroup$ One needs to be very careful to interpret such questions in a coordinate-invariant way. For coordinate invariant characterization of angular momentum of the black hole look up "Komar integrals" and "ADM mass & momentum". $\endgroup$ – Blazej Jun 27 '16 at 20:14

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