Rotating black holes and optical gravity

https://en.wikipedia.org/wiki/Ergosphere

Optical gravity explains in a simple way the ergosphere of a rotating black hole. If we have an optically dense sphere which is rotating very fast, then the local speed of light at a point inside the sphere may be lower than the rotation speed of that point measured in the global coordinates. A fast spinning glass sphere will take even light to rotate with itself in the carousel.

https://en.wikipedia.org/wiki/Penrose_process

One can extract the rotation energy of a black hole through the Penrose process. From where does the energy come from in the process? Does the event horizon of the black hole shrink as energy is extracted from it?

In an extremal black hole, the horizon in the global coordinates is rotating at the speed of light. Suppose that we have an object that passes by the black hole at a speed less than light. Then its interaction with any mass in the part of the horizon close to the object will obviously slow down the rotation of the black hole and transfer angular momentum to the object. The interaction of the object with the far side of the horizon will similarly slow down the rotation of the black hole, and move angular momentum to the object.

If we think frame dragging as a carousel, then the carousel in an extremal black hole rotates at the global speed of light, also to an observer who is far away. The carousel does not slow down when we go further, even though the effect of the frame dragging becomes weaker.