Penrose process

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The Penrose process is a process suggested by Roger Penrose in which energy may be extracted from a rotating black hole. It is made possible by the existence of a region of the Kerr spacetime called the ergoregion, a region in which a particle is necessarily dragged along with the rotating spacetime. In the process, a lump of matter is dropped into the black hole, and once it enters the ergoregion is split into two. The momentum of the two pieces of matter can be arranged so that one piece escapes to infinity, whilst the other falls past the outer event horizon into the hole. The escaping piece of matter can have greater mass-energy that the original infalling piece of matter. In this way, energy is extracted from the Black hole by reducing its angular mometum.

The process obeys the laws of black hole mechanics. A conquence of these laws is that if the process is carried out repeatedly, the black hole can eventually lose all of its angular momentum.

[edit] Details of the Ergoregion

The outer surface of the ergoregion is called the ergosurface and is the surface at which counter rotating (with respect to the black hole rotation) light rays remain at a fixed angular coordinate. 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 gets twirled with it. The inner boundary of the ergoregion is the event horizon, which is the surface beyond which light cannot escape.

Inside this ergoregion, 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 coordinate swap, the energy of the particle can take on both positive and negative values as measured by an observer at infinity.

If particle A enters the ergoregion of a Kerr black hole, then splits into particles B and C, then since conservation of energy still holds and one of the particles is allowed to have negative energy particle B can exit the ergoregion 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, meaning that the black hole is spun down. The maximum amount of energy is extracted if the split happens just outside the event horizon and particle C is counter-rotating as much as possible.

In the opposite process, a black hole can be spun up by sending in particles that do not split up, but instead give their entire angular momentum to the black hole.

The Penrose process has led to speculation that an advanced civilization could generate power by building a city on a fixed structure around the black hole. All their rubbish could be disposed of by sending it in shuttles towards the black hole and ejecting it in the ergoregion. The shuttles could then return to the city with excess energy which could be captured to generate power.