The region around a rotating black hole where spacetime is dragged along with its spin is called the ergosphere.
Frame dragging is predicted by Einstein’s general theory of relativity. A rotating mass twists nearby spacetime, and near a rapidly spinning black hole this effect becomes strong enough that no observer can remain stationary relative to distant space. The ergosphere lies outside the event horizon, so objects can still escape from it.
The ergosphere is not the same as the event horizon. The horizon is the one-way boundary from which light cannot escape, while the ergosphere is a larger, energy-filled region. Roger Penrose showed that an object entering the ergosphere could, in principle, leave with more energy than it carried in by taking energy from the black hole’s rotation. This idea is called the Penrose process.