We can't yet say they "do" rotate or anything else, because we can't
yet say they in fact exist; black holes, though they are on the old
conventional well-accepted end of speculation, are still speculation.
In all cases, though, they are not a "mathematical point" as you
describe. They have mass, charge, and angular momentum. In this
"normal" configuration, the singlularity is a point at the center of
the spherical mass. In this state, rotation is not sufficient to
produce any of the truly bizarre spatio-temporal effects claimed of
toroidial ones. There is also, of course, no model even in the realm
of speculation for any process that might create a toroidial or other
non-ideal black hole.
-- Lee Daniel Crocker <lee@piclab.com> <http://www.piclab.com/lcrocker.html> "All inventions or works of authorship original to me, herein and past, are placed irrevocably in the public domain, and may be used or modified for any purpose, without permission, attribution, or notification."--LDC