December 8, 2011

If the current understanding of astrophysics and relativity is correct, rotating black holes as systems exist within the universe. These systems are formed when a star can no longer support itself against its own gravitational collapse, thereby compressing to a point where normal space-time breaks down and, since stars are rotating in space, in order to preserve conservation of momentum, the black hole itself must have a non-zero rotational angular momentum. [1] In theory, once anything, including energy, passes the event horizon, it cannot return, but, according to Roger Blandford, Roman Znajek, and Roger Penrose, energy can be extracted from the black hole itself. If humanity ever does explore the galaxy, provided that a black hole can be found, it may become a viable power source, but for now, it is an interesting theoretical system that remains, sadly, out of our reach.

In 1977, Blandford and Znajek posed a potential way in which to exploit the magnetic field of a rotating black hole for the purposes of energy extraction. [2] The premise itself is that the material accreting around a black hole would probably be magnetized and increasingly so as the material gets closer to the event horizon. In fact, the magnetic field is so large that it will accelerate an electron to the point where it will begin to radiate gamma-rays, provided that the electron is not beyond the event horizon. In essence, the black hole acts as a massive conductor spinning in a very large magnetic field produced by the accretion disk, where there is a voltage induced between the poles of the black hole and its equator. The ultimate result is that power is dissipated by the slowing down of the rotation of the black hole where the power generated is equal to: [3]

In this equation, P is the estimated power generated,
B is the magnetic field of the accretion disk, and R_{S} is the
Schwarzschild radius of the black hole. This power is dissipated in the
form of electromagnetic radiation and the flow of positions towards the
poles and electrons towards the equators along the magnetic field lines.
[4]

In an example case, for a 10^{8} solar mass
black hole with a 1 T magnetic field, the power generated is
approximately 2.7 × 10^{38} W. [3] In perspective, the
annual energy consumption of the world is estimated around 550
quadrillion BTU or 5 × 10^{20} J. [5] The example case
presented produces more energy in a single second than the entire globe
consumes in a year. While this is a bold claim to make, it is only an
example case where not all the energy produced is extractable as useable
energy. However, at that point, even a system which is less that <
10^{-15} % efficient would be sufficient to supply enough energy
to power the world for a full year.

Of course, the system itself is limited in its lifetime due to the extraction of energy by slowing down the rotation of the black hole. Hence, the system can only exist as long as the black hole has angular momentum, continuing to rotate. At some point, the rotation will cease and the energy source will be unusable.

There are several problems with utilizing this particular method of power extraction. First off, there are currently no patented designs for a method that would convert the motion of the electrons into usable power, most likely due to extreme difficulty in even reaching a black hole. There is a proposal for the usage of a superconducting ring to exploit the magnetic field lines in order to produce power, but, since no patent or scientific paper could be found at this time supporting this, such a design is theoretical at best, mere conjecture at worst. Even if such a system existed however, it would have to be a very specific type of black hole: a rotating black hole with an accretion disk producing a large enough magnetic field. [6] In short, even if getting to a black hole were possible, there are still significant engineering hurdles and other factors that would prevent the easy use of a black hole as a power source.

In 1971, Roger Penrose proposed a way in which to extract energy from a black hole by other means. [7] Unlike the Blandford-Znajek process which relied on magnetism, the Penrose process relied on conservation of momentum. The premise is that if an object in a certain area around a black hole called the ergosphere but not at the event horizon broke apart, with one piece heading towards the center of the black hole and the other piece heading out, the piece that left the black hole would emerge with more energy than it would have entered with.

Similarly to the Blandford-Znajek process, the energy extracted is from the rotation of the black hole, thus limiting the lifespan of this particular generator. At the point where the black hole, ceases to rotate, it will cease to be a source of energy through this process.

There are problems with this method as well. Penrose himself said in his own paper that the method is incredibly inefficient, although later calculations by Chandrasekhar in 1983 showed that the theoretical efficiency could reach 20% extra energy gained. [8] A similar problem to the Blandford-Znajek process arises in that, since there is serious difficulty in even reaching a black hole, there is no patent for a design in which this energy extracted would be converted into usable energy. One can imagine a design in which a massive object is used in the Penrose process where its extra kinetic energy is somehow converted into electrical energy, but that is pure speculation.

While there exist ways for the extraction of energy from a black hole, at this point in time given the current resources and technology available, such an effort would be extremely impractical, due not only to our inability to leave the solar system at this time but also our inability to find ways to exploit these particular behaviors of black holes. While interesting systems in and of themselves, until there is a serious advancement in space technology and research into ways that these processes may be utilized for usable energy production, these will remain simply interesting theoretical systems and remain in the realm of science fiction. However, one day in the far future if humanity can find a way to implement these systems, they may become an incredible source of power.

© Daniel Nagasawa. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

[1] S. M. Carrol, *An Introduction to General
Relativity: Spacetime and Geometry* (Benjamin Cummings, 2003), p
261.

[2] R. D. Blandford and R. L. Znajek,
"Electromagnetic Extraction of Energy from Kerr Black Holes," Monthly
Notices Roy. Astron. Soc. **179**, 433 (1977).

[3] B. W. Carrol and D. A. Ostlie, *An Introduction
to Modern Astrophysics, 2nd ed.* (Benjamin Cummings, 2006), pp.
1114-1115.

[4] K. Thorne, *Black Holes and Time Warps,
Einstein's Outrageous Legacy* (W. W. Norton, 1995), p. 407

[5] "International Energy Outlook 2011," U.S. Energy Information Administration, DOE/EIA-0494(2011), September 2011.

[6] L.-X. Li, "A Toy Model for Blandford-Znajek
Mechanism," Phys. Rev. D **61**, 084016 (2010).

[7] R. Penrose and R. M. Floyd, "Extraction of
Rotational Energy from a Black Hole," Nature Physical Science
**229**, 177 (1971).

[8] S. Chandrasekhar, *Mathematical Theory of Black Holes*
(Oxford University Press, 1983).