# How would a black hole power plant work?

A black hole power plant (BHPP) is something I'll define here as a machine that uses a black hole to convert mass into energy for useful work. As such, it constitutes the 3rd kind of matter-energy power (formerly "nuclear power") humans have entertained, the first two being fission and fusion. Putting aside the fact that the level of technological advancement needed for this is far beyond modern day humans, it seems to be pretty well established that this is possible (and maybe someday inevitable) among physicists. Personally, I feel like I don't understand the proposal because no one has really created a coherent picture of how it would work. To keep this focused, here are my objective questions:

Related to the conversion itself:

• What mechanism of energy release are we talking about? Possibilities include radiation from accretion of material, Hawking radiation, magnetic conversion of rotational energy, and maybe others (EDIT: Manishearth's answer revealed that I don't know the possibilities myself). Can we rule some of these out pragmatically? How well are these mechanisms understood? Do we really have the physics/observations to back them up, or is it still on the forefront of physics?
• How would the energy be harvested? Some possibilities include a thermal cycle (like a Rankine cycle), radiation to electricity conversion (like photovoltaics), magnetically induced currents, and charge movements. Could the particles of emission be too high energy to harness with known materials as a part of the machine structure? That would certainly apply to Hawking radiation from small BHs, do other options have the problem of overly-energetic emissions?

Related to application:

• Is there anything we could use to change the Hawking radiation power output other than the BH mass? Would we be dancing on a knife's edge by using Hawking radiation as a power source? As you should know, a BH evaporation would be a fairly major cosmic event, and to get more power out, one would have to use a smaller BH, which presents a greater risk of catastrophe. This problem could be mitigated by using several BHs so a lower energy throughput would be needed for each, but then that risks BH collision which is also a catastrophic event. Does the spin, charge, or local gravitational potential affect the output? Is there any way for Hawking radiation to be a reasonably safe method of matter to energy conversion (even for an advanced civilization)?
• What are the parameters for the total mass and energy output? Specifically, what would the total energy output divided by mass be, and what would the mass-to-energy conversion efficiency of new in-falling material be? For accretion, I've heard numbers like 30% of the in-falling material can be converted to energy and ejected back into space at the poles... but could we change and control that? How would a BHPP's parameters compare to our sun and current Earth-based power plants?

Sorry I couldn't wrap this up into a single question. I tried. To address the "on topic" concern, I hear people mention that tokomak fusion power research still has many unknowns that are in the domain of physics, as opposed to engineering, which will come later in its development. I tried to edit my question above to be actually physics in nature. I think I speak for most people when I say that I don't understand the vast majority of the physics of BHs. My question here is generally how those physics would play out in a machine that does useful matter to energy conversion.

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Famous last words: That's just an engineering problem. At which point the speaker sneaks off leaving the hard work still to be done. –  dmckee Feb 10 '12 at 20:08
Bhpps dont use hawking radiation. They extract ROTATIONAL energy from a spinning black hole (lots if mass, so lots of angular momentum/energy to be extracted). I doubt that hawking radiation would be efficient. –  Manishearth Feb 11 '12 at 3:05

I don't know about extracting mass-energy from inside the black hole, it seeps pretty inefficient to me. Hawking radiation isn't that powerful (as well as still being highly hypothetical), building a Dyson sphere around a star is better. Remember, black holes, are, well, black. If there was enough hawking radiation, they would cease to be black and would shine like stars.

The efficient way to extract energy from a black hole is to extract its rotational energy. 20% [1] of a (rotating) black hole's mass-energy is in the form of rotational energy. This energy is not stored inside the black hole, rather it is stored in the swirl of space outside the black hole (In the Ergosphere). We can extract this energy by threading magnetic filed lines through the black hole. The swirl of space swirls the magnetic fields, and this swirl creates current (I'm not sure of the exact treatment of this, classically it would be some form of electromagnetic induction, but this isn't classical physics.). The current flows along the field lines, and can be picked up.

Here's a picture from [1]:

UPDATE: See this also.

[1] Black Holes and Time Warps, Kip Thorne. Pg 53

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This is exciting! Apparently I thought that I knew a great deal more than I actually did. I will have to edit my question to allow for more processes. You mention a possibility that I didn't even think to mention. The superconducting coils do look like they come possibly perilously close to the BH, but maybe not. I imagine this idea could use comparatively "small" BHs and it's not clear how significant how far out the magnetic influence is compared to the gravitational. The current lines are difficult to swallow - it doesn't look like inductive current. –  Alan Rominger Feb 11 '12 at 16:32
Arxiv link discussing hawking radiation power generation (no claims as to quality): arxiv.org/abs/0908.1803v1 –  user2963 Feb 11 '12 at 17:04
@Zassounotsukushi: Even I find it difficult to swallow. It was mentioned that it was by the same mechanism that powers quasars. I vaguely remember something called the blandford-znajek process for quasars where there is a similar current. Ill look it up tomorrow. The net doesnt seem to have much on it. –  Manishearth Feb 11 '12 at 17:25
@Zassounotsukushi Alright, wherever I look, the "current" part of the Blandford-znajek process seems to taken almost for granted. It seems that the strong magnetic field lines accelerate the electron/charged particle, and the swirl of space does something or the other to it. The end result is that a potential difference is developed and there's a current. –  Manishearth Feb 12 '12 at 11:00
I think we need someone who understands GR better to finish this off. –  Manishearth Feb 12 '12 at 11:01

With this answer, I am going to list some of my notes from the paper that @zephyr posted as a comment, http://arxiv.org/abs/0908.1803v1. Using Hawking radiation as a means of mass-to-energy conversion seems, in a word, absurd. The paper, however, addressed exactly that for use in powering a manned spaceship to the stars.

# Hawking Radiation as a thrust source

Firstly, let me list the parameters of the BH discussed in the paper:

• mass of $10^{12} kg$
• radius of $10^{-10} m$, or $10^{-18} m$, it's not entirely clear
• power of $P=a f(T) / R^2$, which is different depending on the numbers I try from the paper, my first try gives me $13 W$, which indicates that the radius of $10^{-10} m$ is too big.

Good points

Such a spaceship, by the way, is an extraordinarily energy-intensive activity. A major fraction of the mass of any such spaceship would necessarily have to be converted to energy for the idea to be workable. Thus, it is necessary for the trust device to have very high mass-to-energy conversion efficiency for this process. This is among the reasons that Hawking radiation may be the only viable options for certain trips.

When thinking about designing a spaceship, our considerations go beyond the craft itself. Earth-bound or solar-bound activities will be needed to build it and prepare the energy source. The paper compares Hawking radiation to an antimatter rocket. It makes the general claim that theorists don't predict the antimatter production efficiency to exceed $10^4$ energy input to mass created. Now, all of the mass of the antimatter will be converted to photon propellent in-service in the spaceship. The efficiency quantification for an artificial black hole is a little more complicated. So I made a picture.

Basically, you throw together some amount of mass so that it compresses tighter than its event horizon and you have a black hole. Obviously, this would be a very energetic process to do, so we have to include the kinetic energy used to throw this matter together to an extremely small point. As you're using it, though, you can add as much mass as you want to the BH with relative ease because once it's in the event horizon, it has added to the mass. Hawking radiation will be emitted continuously (whether you want it to or not), and at the end of the trip you'll be left with some mass as a BH that you didn't use. This is important to include for a spaceship because for a spaceship the matter-energy to energy conversion matters. For civilian power, generally the energy to energy conversion matters. I defined the matter-to-energy conversion above, but the energy-to-energy efficiency would be:

$$\eta = \frac{M+E+M'-M''}{E}$$

The point I'm getting to is that the mass-to-energy conversion efficiency will be close to 1, similar to anti-matter. The energy-to-energy conversion will be vastly greater than 1, as opposed to $10^{-4}$ for the case of anti-matter. Based on pure energetics, BHs would be very efficient, light, and ideal for a interstellar thrust source.

The other major reason for looking at Hawking radiation from artificial black holes is that they have very good confinement. Using anti-matter would require actively confining the antimatter, for which the prospects do not look good. Should the active confinement methods fail, there will be a spectacular explosion that destroys the spacecraft and the local cosmic neighborhood. A BH, on the other hand, is passively confined by gravity. If left to sit for long enough, yes, it can evaporate and destroy just as much, but that will take time to happen.

Drawbacks

Firstly, in order to get the power level needed, the BH would have to be "subatomic black hole" (SBH), with a radius less than $10^{-10} m$. Apparently, we don't know exactly how much power a given mass SBH would emit, that requires basically quantum gravity physics models, and those are not completely decided upon.

Also, apparently, such a SBH would emit some of its mass as mass, not energy. This means that mass would not be converted to thrust for a spacecraft and would not be converted to useful energy in a civilian power plant type application. Also, neutrinos would be created and emitted isotropically, contributing nothing to either thrust or useful energy.

The temperature of the SBH would be very high apparently, somewhere in the range of $0.06 GeV$ and $100 GeV$ for the parameters the paper discussed. These energies will have a large multiplier for calculating material radiation damage. Shielding would also be difficult.

The mass entertained in the paper is $10^{12} kg$, and to create the black hole, this would have to be accelerated/compressed into a subatomic radius. At the risk of sounding snarky, this doesn't sound easy. This is basically saying that if you can compress Mount Everest into the volume of a single atom you can have free energy. One method discussed is to use "converging x-ray lasers" to do this. Apparently self-gravitation may help focus them to a point. So that's one bit of good news.

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Recommend you look up black hole on Wikipedia. All of your open questions are answered there. Also look up Hawking radiation. –  Andrew Palfreyman Jan 24 at 2:54
How could you accelerate the black hole? –  Kevin Kostlan Feb 26 at 13:55
@KevinKostlan reflect the hawking radiation on a single side back into the black hole to give it a net thrust –  Inverse Oct 27 at 4:49

## protected by Qmechanic♦May 11 '13 at 21:47

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