Final answer:
The question regarding the change in the event horizon if a black hole begins rotating does not have a straightforward answer; the radius depends on the mass, and rotation causes complex shape changes rather than simple expansion or contraction.
Step-by-step explanation:
If a black hole changes from having no rotation to rotating at its maximum speed, the event horizon of the black hole does not simply expand or contract based solely on its rotation; instead, more complex changes occur due to the Kerr metric in general relativity. However, the given options do not thoroughly reflect this complexity.
The event horizon is the boundary around a black hole past which no information can escape. Typically, the radius of this event horizon, known as the Schwarzschild radius, depends only on the mass of the black hole.
When a black hole begins to rotate, it becomes a Kerr black hole, which features an oblate event horizon that is flattened at the poles rather than spherical. Adding rotation can actually reduce the size of the event horizon along the poles, but globally speaking, it changes shape rather than expands or contracts in a simple manner.
In context with our understanding of the conservation of angular momentum, the angular velocity of a black hole that begins rotating will increase, which in turn affects its event horizon and moment of inertia. This might seem similar to the concept wherein if the moment of inertia of an isolated system increases, its angular velocity decreases, as stated in physics.