The region around a rotating black hole where spacetime is dragged is the ergosphere.
A rotating black hole twists nearby spacetime in the direction of its spin, an effect called frame-dragging or the Lense–Thirring effect. Inside the ergosphere, this dragging becomes so strong that no object can remain stationary relative to a distant observer; everything must co-rotate with the black hole.
The ergosphere lies outside the event horizon, so entering it does not necessarily mean falling permanently into the black hole. In theory, an object can enter, interact with the black hole’s rotation, and escape carrying away some of its rotational energy. This idea, proposed by Roger Penrose in 1969, is called the Penrose process.
The ergosphere is not the same as the event horizon. The horizon is the point of no return, while the ergosphere is a wider region that touches the horizon at the poles and extends farthest outward around the equator. A non-rotating black hole has no ergosphere.