Penrose process

# Penrose process

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Encyclopedia
The Penrose process is a process theorised by Roger Penrose
Roger Penrose
Sir Roger Penrose OM FRS is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford and Emeritus Fellow of Wadham College...

wherein energy can be extracted from a rotating black hole
Rotating black hole
A rotating black hole is a black hole that possesses spin angular momentum.-Types of black holes:There are four known, exact, black hole solutions to Einstein's equations, which describe gravity in General Relativity. Two of these rotate...

. That extraction is made possible because the rotational energy of the black hole is located, not inside the event horizon
Event horizon
In general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer. In layman's terms it is defined as "the point of no return" i.e. the point at which the gravitational pull becomes so great as to make escape impossible. The most common case...

of the black hole, but on the outside of it in a region of the Kerr
Kerr metric
The Kerr metric describes the geometry of empty spacetime around an uncharged axially-symmetric black-hole with an event horizon which is topologically a sphere. The Kerr metric is an exact solution of the Einstein field equations of general relativity; these equations are highly non-linear, which...

spacetime
Spacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

called the ergosphere
Ergosphere
The ergosphere is a region located outside a rotating black hole. Its name is derived from the Greek word ergon, which means “work”. It received this name because it is theoretically possible to extract energy and mass from the black hole in this region...

, a region in which a particle is necessarily propelled in locomotive concurrence with the rotating spacetime. All objects in the ergosphere become dragged by a rotating spacetime
Frame-dragging
Einstein's general theory of relativity predicts that non-static, stationary mass-energy distributions affect spacetime in a peculiar way giving rise to a phenomenon usually known as frame-dragging...

. In the process, a lump of matter enters into the ergosphere
Ergosphere
The ergosphere is a region located outside a rotating black hole. Its name is derived from the Greek word ergon, which means “work”. It received this name because it is theoretically possible to extract energy and mass from the black hole in this region...

of the black hole, and once it enters the ergosphere, it 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, whereas the infalling piece has negative mass-energy. 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
Black hole thermodynamics
In physics, black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons...

. 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. Demetrios Christodoulou
Demetrios Christodoulou
Demetrios Christodoulou is a Greek mathematician and physicist, who first became well known for his proof, together with Sergiu Klainerman, of the nonlinear stability of the Minkowski spacetime...

calculated an upper bound for the amount of energy that can be extracted by the Penrose process.

## 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.