Rotating space does not imply time travel. For one thing, time in our space does not match time in the ergosphere. This results because space near the rotating black hole is traveling faster than light speed in our static universe. But at the interface between the ergosphere and our universe, the velocities of the ergosphere and of our standard static space are equal. That is, v = 0 since our space is not rotating relative to the ergosphere.
Time travel occurs when time outside the traveler's reference frame goes faster or slower than time within the travelers frame. Although travel into the past is impossible, travel into the future is possible when the traveler's velocity v --> c the speed of light. But note, this is the traveler, not space that is going at velocity v. And our static space, outside the ergosphere, is not being dragged; so there is no velocity a traveler can gain from it. Thus, there is no time travel implied by the faster than light spinning of the ergosphere because that spinning does not extend into our static space.
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