  A highly accurate computer program is used to study axially symmetric and
stationary spacetimes containing a Black Hole surrounded by a ring of matter.
It is shown that the matter ring affects the properties of the Black Hole
drastically. In particular, the absolute value of the ratio of the Black Hole's
angular momentum to the square of its mass not only exceeds one, but can be
greater than ten thousand (|J|/M^2 > 10^4). Indeed, the numerical evidence
suggests that this quantity is unbounded.
