Definitions

# Penrose process

The Penrose process (also called Penrose mechanism) is a process theorised by Roger Penrose wherein energy can be extracted from a rotating black hole. That extraction is made possible by the existence of a region of the Kerr spacetime called the ergoregion, a region in which a particle is necessarily propelled in locomotive concurrence with the rotating spacetime. In the process, a lump of matter enters into the ergoregion of 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 possibly have greater mass-energy than the original infalling piece of matter. In summary, the process results in a decrease in the angular momentum of the black hole, and that reduction corresponds to a transference of energy whereby the momentum lost is converted to energy extracted.

The process obeys the laws of black hole mechanics. A consequence of these laws is that if the process is performed repeatedly, the black hole can eventually lose all of its angular momentum, becoming rotationally stationary.

## Details of the Ergoregion

The outer surface of the ergoregion 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 ergoregion is the event horizon, that event horizon being the spatial perimeter 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 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 ergoregion 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 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, 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.

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. (This speculative arrangement does not specify how the shuttles would actually capture the energy, however.)

## References

Misner, Thorne, and Wheeler, Gravitation, Freeman and Company, 1973.

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