Lense-Thirring Effect
Just as a spinning ball in a viscous fluid drags the fluid around it, a rotating black hole drags spacetime itself. This phenomenon is known as frame dragging or the Lense-Thirring effect. Any object entering the vicinity of a Kerr black hole is forced to rotate in the same direction as the black hole, regardless of its initial motion. Even light cannot travel against the spin inside a certain boundary.
The Ergosphere
The region where frame dragging is so strong that no observer can remain stationary relative to distant stars is called the ergosphere. It lies between the outer event horizon and the static limit surface. Inside the ergosphere, the time-like Killing vector becomes space-like, meaning that moving forward in time necessarily involves moving in the direction of the black hole's rotation.
Static Limit vs. Event Horizon
In the Schwarzschild metric, the event horizon is the only critical radius. In the Kerr metric, there are two. The outer boundary of the ergosphere is the 'static limit,' where the required orbital velocity equals the speed of light. The event horizon lies deeper inside. Between these two surfaces is the ergoregion, where escape is still possible, but co-rotation is mandatory.