Details of The Ergosphere
The outer surface of the ergosphere is described as the ergosurface and it is the surface at which light-rays that are counter-rotating (with respect to the black hole rotation) remain at a fixed angular coordinate, according to an external observer. Since massive particles necessarily travel slower than the speed of light, massive particles must rotate with respect to a stationary observer "at infinity". A way to picture this is by turning a fork on a flat linen sheet; as the fork rotates, the linen becomes twirled with it, i.e. the innermost rotation propagates outwards resulting in the distortion of a wider area. The inner boundary of the ergosphere is the event horizon, that event horizon being the spatial perimeter beyond which light cannot escape.
Inside this ergosphere, the time and one of the angular coordinates swap meaning (time becomes angle and angle becomes time) because timelike coordinates have only a single direction (and remember the particle is necessarily rotating with the black hole in a single direction only). Because of this weird and unusual coordinate swap, the energy of the particle can assume both positive and negative values as measured by an observer at infinity.
If particle A enters the ergosphere of a Kerr black hole, then splits into particles B and C, then the consequence (given the assumptions that conservation of energy still holds and one of the particles is allowed to have negative energy) will be that particle B can exit the ergosphere with more energy than particle A while particle C goes into the black hole, i.e. E(A)=E(B)+E(C) and say E(C)<0, then E(B)>E(A).
In this way, rotational energy is extracted from the black hole, resulting in the black hole being spun down to a lower rotational speed. The maximum amount of energy is extracted if the split occurs just outside the event horizon and if particle C is counter-rotating to the greatest extent possible.
In the opposite process, a black hole can be spun up (its rotational speed increased) by sending in particles that do not split up, but instead give their entire angular momentum to the black hole.
Read more about this topic: Penrose Process
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