Ergosphere

Summary

The ergosphere of a rotating black hole is the region outside the event horizon where nothing can stay at rest relative to distant observers. There the time-translation Killing vector field becomes spacelike, so every observer is dragged around with the rotation of the hole. In the Kerr metric it is a flattened region that touches the horizon at the poles and reaches out to $r = 2M$ at the equator. Particles inside it can have negative energy, which makes the Penrose process possible.