Q: How can a black hole have spin? How is it possible, or even meaningful, to say that a black hole has spin? (Tangentially, if the singularity is assumed to be a point, it must have either zero or infinite angular momentum, in both cases violating conservation of momentum.) No information can be communicated out of the black hole about the singularity's spin, but even so, [to my admissibly limited knowledge] spacetime cannot be twisted, only bent. The event horizon itself is uniform and featureless, and has no properties except for size, which can only be indirectly observed as optical distortion. Magnetic field cannot escape from it. Given such restrictive conditions, what is there to suggest spin?

A: As I am not allowed to comment for lack of reputation and cannot find a way to message I would like to point you to a reasonably recent source on the Kerr metric. I am by no means an expert  but from what I have read and from what I understand the "Lines" of space time do twist and become unstable at the Cauchy Horizon. From what I gather the rotation isn't necessarily from the singularity but from the entire "mass" beyond the Cauchy horizon thus allowing the black hole to rotate and have an angular velocity that is not infinite. This however could be argued as infinite could very well be defined as the seed of light that several super massive black hole have been measured to be spinning at or near. The following are a few resources that I have found to be helpful in my own limited understanding of black holes and space-time.
http://www.eftaylor.com/pub/SpinNEW.pdf A wonderful project that illustrates and explains much theory as it goes.
http://www.gothosenterprises.com/black_holes/rotating_black_hole.html Very nice graphical representations.
http://news.discovery.com/space/could-black-holes-give-birth-to-planck-stars-140211.htm This article explains much better some of what I was trying to get across.
http://www.astro.sunysb.edu/rosalba/astro2030/KerrBH.pdf Rather simplistic not highly recommended but it is there and would impart a base understanding with which to read the others.
