Yes, the rotation of a black hole contributes to time dilation beyond the effects of normal gravitational time dilation. The rotation of a black hole can increase the time dilation experienced by an observer compared to what would be expected from the black hole's mass alone.
In general relativity, a rotating black hole possesses a property called frame dragging or the Lense-Thirring effect. This effect arises due to the dragging of spacetime around the rotating black hole. As a result, the rotation of a black hole can induce additional time dilation for observers in its vicinity.
Near a rotating black hole, the frame dragging effect causes spacetime to become "twisted" or "dragged" in the direction of rotation. As a consequence, the paths of particles or observers near the black hole are influenced by this twisted spacetime geometry.
Specifically, the rotation of a black hole affects the motion of objects that are orbiting or moving in the vicinity of the black hole. For example, the rotation can cause an orbiting object or an observer in a close orbit to experience an additional precession in their path or an apparent shift in the direction of motion.
This additional precession due to the black hole's rotation contributes to an enhanced time dilation effect. Observers closer to the black hole experience stronger frame dragging and, consequently, greater time dilation compared to observers farther away.
In summary, the rotation of a black hole contributes to time dilation through the frame dragging effect, causing additional effects beyond the standard gravitational time dilation associated with the black hole's mass. This effect is particularly significant in the vicinity of the black hole and can increase the time dilation experienced by nearby observers.