Penrose process

The Penrose process (also called Penrose mechanism) is theorised by Roger Penrose as a means whereby energy can be extracted from a rotating black hole.[1][2] That extraction can occur if the rotational energy of the black hole is located not inside the event horizon but outside in a region of the Kerr spacetime called the ergosphere in which any particle is necessarily propelled in locomotive concurrence with the rotating spacetime. All objects in the ergosphere become dragged by a rotating spacetime.

In the process, a lump of matter entering the ergosphere is triggered to split into two parts. For example, the matter might be made of two parts that separate by firing an explosive or rocket which pushes its halves apart. The momentum of the two pieces of matter when they separate can be arranged so that one piece escapes from the black hole (it "escapes to infinity"), whilst the other falls past the event horizon into the black hole. With careful arrangement, the escaping piece of matter can be made to have greater mass-energy than the original piece of matter, and the infalling piece gets negative mass-energy. Although momentum is conserved the effect is that more energy can be extracted than was originally provided, the difference being provided by the black hole itself.

In summary, the process results in a slight decrease in the angular momentum of the black hole, which corresponds to a transference of energy to the matter. The momentum lost is converted to energy extracted.

The maximum amount of energy gain possible for a single particle via this process is 20.7% in the case of an uncharged black hole.[3] 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 non-rotating, i.e. a Schwarzschild black hole. In this case the theoretical maximum energy that can be extracted from an uncharged black hole is 29% of its original mass.[4] Larger efficiencies are possible for charged rotating black holes.[5]

In 1971, the theoretical physicist Yakov Zeldovich translated this idea of rotational superradiance from a rotating black hole to that of a rotating absorber such as a metallic cylinder,[6] and that mechanism was experimentally verified in 2020 in the case of acoustic waves.[7]

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 will necessarily 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 (the particle rotates with the black hole in a single direction only). Because of this 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.

See also

• Blandford–Znajek process, one of the best explanations for how quasars are powered
• Hawking radiation, black-body radiation believed to be emitted by black holes due to quantum effects
• High Life, a 2018 science-fiction film that includes a mission to harness the process

References

1. R. Penrose and R. M. Floyd, "Extraction of Rotational Energy from a Black Hole", Nature Physical Science 229, 177 (1971).
2. Misner, Thorne, and Wheeler, Gravitation, Freeman and Company, 1973.
3. Chandrasekhar, pg. 369
4. Carroll, pg. 271
5. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.512.1400&rep=rep1&type=pdf Energetics of the Kerr–Newman Black Hole by the Penrose Process; Manjiri Bhat, Sanjeev Dhurandhar & Naresh Dadhich; J. Astrophys. Astr. (1985) 6, 85–100 – www.ias.ac.in
6. Physicists Verify Half-Century-Old Theory about Rotating Black Holes www.sci-news.com, 24 June 2020
7. Amplification of waves from a rotating body www.nature.com, Published: 22 June 2020, retrieved 28 June 2020

Further reading

• Chandrasekhar, Subrahmanyan (1999). Mathematical Theory of Black Holes. Oxford University Press. ISBN 0-19-850370-9.CS1 maint: ref=harv (link)
• Carroll, Sean (2003). Spacetime and Geometry: An Introduction to General Relativity. ISBN 0-8053-8732-3.