A rotating black hole is a flywheel, and in principle you can steal some of its spin. That is the idea behind the Penrose process, theorised by Sir Roger Penrose as a way to pull energy out of a rotating black hole.
The ergosphere
The trick depends on the ergosphere, a region of spacetime around the black hole that its rotation drags along faster than the speed of light. To an outside observer, anything inside is forced to move in the direction the black hole turns. Even light cannot keep up with the rotation there.
Inside that region, matter can carry negative energy, as long as it moves against the rotation fast enough. The Penrose mechanism exploits this. An object dives into the ergosphere, dumps a piece that has been given negative energy, and comes back out with more energy than it took in.
How the extraction works
Picture a working body falling into the ergosphere. At its lowest point it fires a propellant backwards. Because of frame-dragging, a faraway observer sees both pieces keep moving forward, at different speeds. The slowed propellant falls to the event horizon. The rest of the body, sped up, flies away carrying an excess of energy that more than covers the propellant lost and the energy spent firing it.
The energy comes from the black hole’s rotation, so the hole spins down to a lower speed. Maximum extraction happens when the black hole turns at the maximal rate, the object just grazes the event horizon and splits into two packets of light, one moving forwards and escaping, the other moving backwards and falling in.
The limits
The gain is capped. In the original, classical version, one particle decay can yield at most 20.7 percent of its mass in extra energy, and that is for an uncharged black hole at maximal rotation. Because the energy is drawn from the spin, the total is capped too: no more than 29 percent of the original mass for an uncharged black hole. Charged rotating black holes would allow higher efficiencies.
There is also a related move that goes the other way. A black hole can be spun up by sending in particles that do not split, so they hand over all of their angular momentum. It is not simply the Penrose process in reverse, since throwing material in raises the black hole’s entropy either way.
