> But how can we tell if a mathematical point is rotating or not?
As Lee Daniel Crocker pointed out, black holes are not points. They
are a pattern of spacetime, and rotates in all physically reasonable
models. A simple way of testing if a black hole rotates (and how fast)
is to drop a small object from towards it. If the object begins to
deviate from a straight fall, then the hole rotates and the deviation
and direction of deviation can be used to calculate the angular
momentum.
I think there are some popular explanations of this in Pickover's
_Black Holes: A Travellers Guide_. There is also (of course) a more
detailled treatment in Misner, Thorne, Wheeler's _Gravity_.
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