The region outside a rotating black hole where no stationary observer can exist is the ergosphere. It is produced by frame-dragging: the rotating black hole twists nearby spacetime and forces matter and light to rotate along with it.
Inside the ergosphere, an observer cannot remain fixed relative to distant stars. To appear stationary from far away, the observer would need to move against the dragged spacetime at an impossible speed exceeding the local speed of light. Unlike the event horizon, the ergosphere is not necessarily a point of no return; objects can still escape from it.
The ergosphere surrounds the event horizon of a Kerr black hole and meets the horizon at the poles. Its outer boundary is called the static limit or ergosurface. The region can therefore be distinguished geometrically from the horizon itself.
The ergosphere also permits the Penrose process, proposed in 1969, in which an object splits and one part falls into the black hole with negative energy relative to infinity. The escaping part can carry away more energy than the original object supplied.