Orbital Black Hole Power Plant

[DatBurnTho11]

------THE SCENARIO-------
Ever since I heard of Hawking radiation, I've long held a fantasy of harnessing the power emanated from a black hole into useful energy. It's like direct matter to energy conversion!

So, to explore whether this is at all possible - I propose this scenario: Let's just say that modern day humans happened to find a small (gravitationally-insignificant) black hole in a stable near-Earth orbit. The black hole would be so small as to be very hot and thus emit black-body radiation per Hawking's theorem.

Would it be worthwhile to construct some facility to harness the energy being emitted from the black hole? If so, how could we do this?



-----MY TAKE ON IT------
The most efficient EM radiation to electricity converters I know of are photovoltaics. My knowledge on this subject is very limited so I'll assume that photovoltaics operate within the Shockley-Queisser limit which I approximate to be 30% efficient in converting light energy from 0.5 eV to 3 eV to electrical energy.

For a non-rotating, non-charged blackhole, the mass and surface area are directly related to temperature. Temperature also defines the intensity of a black body radiator. With all this, it's trivial to define a relationship between electric power recovered from the black hole and temperature.

Elec. Power = 0.3 * Integrate [intensity * surface area (for a given temp)] from frequency equivalents of 0.5 eV to 3 eV
Elec. Power = Function of Temp

I wrote a little Matlab script to find the optimum temperature to maximize electric power recovered and got some very disappointing results:

Code: Select all

Optimum Temperature:        1.544e+004 K
Mass of Black Hole:         7.950e+018 kg
Radius of Black Hole:       1.181e-008 m
Total Power Emitted:        1.794e-006 W
Total Elec Power Received:  1.238e-007 W

I thought for sure something must be wrong about this! A tenth of a micro-watt! And only 10,000 degrees! My program indicates that if the black hole gets any hotter it begins to get so small that the increased intensity still results in lower power outputs...

Was there some flaw in my assumptions that might have lead to this? Or is my dream of a black-hole power-plant really not that realistic?

[Covenant]

Would it be worthwhile to construct some facility to harness the energy being emitted from the black hole?

Not really. The energy required to build this facility would be huge, and the technology very advanced. To make that kind of a project possible presumes you've got the tech to do other, lesser projects that would be more efficient. The point at which you're generating energy from a black hole you could just as easily be generating it from a stable star, like the one we already have.

Or is my dream of a black-hole power-plant really not that realistic?

There's a difference between possible and realistic, really. The problem with 99% of the super-science magical technologies is that there's something mundane and more effective for the same level of technology. Plasma weapons are a good example as something which people ALWAYS like to add into a setting, but as the information on this and other sites will explain, make zero logical sense from either a functional or even probably existence standpoint.

Black hole reactors are similar. If you can build something in space capable of doing the kind of energy extraction and transmission to Earth like you're talking about then you need to assume that we're advanced enough to do other things, like build solar collectors in space. A solar collector in space would provide tons of advantages over a black hole reactor. Even if you were getting 100 times more energy from the black hole than a collector, you could probably build thousands of solar collectors if energy was so important we didn't want to generate it dirtside.

If you absolutely want to write a story where we build a black-hole reactor you can always try to handwave a kind of magical radiation or something that you need to absorb or something. Otherwise, yeah, I'd probably say it just sounds shoe-horned in there.

[Ariphaos]

If you can make a statite that can absorb a hundred times the energy, you can alternately just put it ten times closer to the Sun.

[Lord of the Abyss]

If you absolutely want to write a story where we build a black-hole reactor you can always try to handwave a kind of magical radiation or something that you need to absorb or something.

I recall a short story where they turned a micro black hole that drifted near Earth into a power plant. It turned out though that was actually just a cover story to avoid panic; the real reason they turned it into a power plant was because it was so small that it was on the verge of runaway Hawking decay and they had to build all that expensive apparatus just to feed it enough matter to keep it from going up in a flash and frying Earth. It producing energy was just a bonus.

[Kuroneko]

For a black hole of large specific angular momentum, the Penrose process can extract energy from it. For a slowly rotating black hole, things are a bit different. I doubt it will work effectively for small black holes, but it's you can look into such alternatives if you're interested.

The black hole event horizon can be modeled as a two-dimensional viscous fluid that's electrically but not thermally conductive. Accreting matter will be driven into a disk by a combination of gravitomagnetic and viscous forces. If the disk is ionized, it will electrically conduct.

At this point, it should be clear what this would look like for a slowly rotating black hole: you have a conducting sphere, so if you have a conductive path to its pole, you can pass current to the pole, along along the surface, and out of the flat conductive disk surrounding it. Apply an magnetic field, and you have the simplest rotor for an electric motor.

If the black hole can keep the disk hot enough to strongly ionize it, it will be highly electrically conductive, and therefore "freeze" the magnetic field, except for occasional magnetic reconnection. For a strong magnetic field, the field lines act as wires. The black hole can now serve as the rotor in an electrical generator.

The monograph on black holes by Thorne, Price, and MacDonald is interesting, and it references the Blandford-Znajek effect for power generation. I'm sure there are both newer and more in-depth analyses of this elsewhere, but I'm not familiar enough with the literature.

[Zaune]

Not really. The energy required to build this facility would be huge, and the technology very advanced. To make that kind of a project possible presumes you've got the tech to do other, lesser projects that would be more efficient. The point at which you're generating energy from a black hole you could just as easily be generating it from a stable star, like the one we already have.

And perhaps more importantly, it involves sticking a miniature black hole in near-Earth orbit. Can you even imagine trying to write up the risk-assessment documentation for the planning application?

If you absolutely want to write a story where we build a black-hole reactor you can always try to handwave a kind of magical radiation or something that you need to absorb or something. Otherwise, yeah, I'd probably say it just sounds shoe-horned in there.

Probably the sanest take on this can be found in the short story The Clockwork Atom Bomb by Dominic Green (downloadable for free from here, audiobook version here), which expands upon just how horribly bad an idea this would be.

[Elheru Aran]

Random observation; doesn't Dan Simmons have black-hole power sources used in his Ilium/Olympos books? The main thing I remember was black-hole warheads in a submarine, but I think I remember them being used for power... I could be wrong though. They do harp upon the warheads being excessively/insanely powerful (as in one of them could destroy the Earth, and the submarine had over twenty...)

[DatBurnTho11]

Thanks for the quick responses guys! I guess this is more of a fun intellectual thought experiment than anything with potential practical use.

@Kuroneko - I hadn't thought of using the black hole as a rotating magnet for electric generation. You'll need to help me out though, I can understand how an accretion disk of charged matter rotating around the black hole might create a magnetic dipole on the axis of its rotation. But wouldn't we need the whole dipole to rotate to get energy out of it? Or do we have something different that would make the structure rotate.

I'm definitely going to check out some of those e-books. Thanks for the links.

Lol, I feel kind of silly doing all that math if the basic concept is flawed - I knew this was a engineering based board and wanted to put my new MatLab skills to work I guess, haha!

[Steel]

Well how about a simpler solution to generating power from the black hole. When something falls into a black hole its change in GPE can be around half its rest mass ie ~0.5mc^2

So if you wind a long rope round an axle and then dangle one end towards the black hole you can get the black hole to turn a generator hooked up to the end of your axle. Slight issues may arise with the rope being annihilated by shear forces (significantly) before reaching the event horizon, but this sort of thing could be alleviated by making the rope out of carbon nanotubes or whatever.

Turning this on and off is as simple as cutting the rope, and increasing or decreasing the output you just dangle more ropes in (or use stronger ones) I'd recommend having pairs of generators on opposite sides if you do this in space so that you don't have your generators drift towards the hole over time.

[Sriad]

I love me some black holes.

I'm not sure exactly what went wrong with your program, but as long as your photovoltaics can handle extremely hard gamma rays (say, neighborhood of 1.8×10^26 hz) there's no physics-based reason you can't get very substantial power generation. Engineering is a different problem though. Feeding 1.5 kilograms of whatever into a point about 1/10th of an attometer across every second would be tricky even if that point wasn't spewing hard radiation. (those numbers reflect a black hole that would take a year to evaporate.) Maybe you were limiting your photovoltaics' properties, but that seems like a step to far into the hard SF... and even if you're determined to stick to it you could conceivably power down the radiation by shooting it into some other object that would radiate easier to handle wavelengths.

I'd suggest you get it spinning REALLY FUCKING FAST and aim a particle accelerator beam (or a hundred) edge on at the event horizon in the direction of rotation to keep it spinning; because the black hole is flattened it most radiation will (IIRC... maybe) escape along the rotation axis. You'll have to deal with a lot of frame-dragging but at least your apparatus for getting stuff in can mostly be in a different place than your tech for getting energy from what comes out.

Note that the explosion of a popping quantum black hole is surprisingly "small": only 20 teratons (1/5th of the Chicxulub meteor impact) for the last minute of its life. You'll still want it well away from Earth, but Earth-sun L4 or 5 would be quite far enough that it wouldn't be troublesome.

Numbers taken from this handy little calculator.

Like Covenant mentioned there are much simpler ways to get energy given the tech base you'd need, but it's possible and has a lot more "gee-wow" factor than really good solar panels near the sun.