Extracting energy from a black hole

The Penrose process is a process theorised by Roger Penrose wherein energy can be extracted from a rotating black hole. That extraction is made possible because the rotational energy of the black hole is located, not inside the event horizon of the black hole, but on the outside of it in a region of the Kerr spacetime called the ergosphere, 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. In the process, a lump of matter enters into the ergosphere 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. 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 calculated an upper bound for the amount of energy that can be extracted by the Penrose process.

And Reva-Kay Williams used the Penrose process to explain the collimated and asymmetrycal jets from some space objects, like rotating black holes:

Over the past three decays, since the discovery of quasars, mounting observational evidence has accumulated that black holes indeed exist in nature. In this paper, I present a theoretical and numerical (Monte Carlo) fully relativistic 4-D analysis of Penrose scattering processes (Compton and $\gamma \gamma \rightarrow e^+ e^-$) in the ergosphere of a supermassive Kerr (rotating) black hole. These model calculations surprisingly reveal that the observed high energies and luminosities of quasars and other AGNs, the collimated jets about the polar axis, and the asymmetrical jets (which can be enhanced by relativistic Doppler beaming effects), all, are inherent properties of rotating black holes. That is, from this analysis, it is shown that the Penrose scattered escaping particles exhibit tightly wounded coil-like cone distributions (highly collimated jet distributions) about the polar axis, with helical polar angles of escape varying from 0.5o to 30o for the highest energy particles. It is also shown that the gravitomagnetic (GM) field, which causes the dragging of inertial frames, exerts a force acting on the momentum vectors of the incident and scattered particles, causing the particle emission to be asymmetrical above and below the equatorial plane, thus breaking the reflection symmetry of the Kerr metric (above and below the equatorial plane). When the accretion disk is assumed to be a two-temperature bistable thin disk/ion corona, recently referred to as an advection dominated accretion flow (ADAF), energies as high as 54 GeV can be attained by these Penrose processes alone; and when relativistic beaming is included, energies in the TeV range can be achieved, agreeing with observations of some BL Lac objects. When this model is applied specifically to quasars 3C 279 and 3C 273, their observed high energy luminosity spectra can be duplicated and explained. Moreover, this Penrose energy extraction model can be applied to any size black hole, irrespective of the mass, and, thus, suggests a complete theory for the extraction of energy from a black hole.

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Williams, R.K., High Energy-Momentum Extraction from Rotating Black Holes Using the Penrose Mechanism. American Astronomical Society, 195th AAS Meeting, #134.02; Bulletin of the American Astronomical Society, Vol. 32, p.881
Reva Kay Williams (2002). The Gravitomagnetic Field and Penrose Processes, arXiv: astro-ph/0203421v2
Penrose, R., Gravitational Collapse: the Role of General Relativity. Rivista del Nuovo Cimento, Numero Speziale I, 252 (1969) (pdf)