Your Neighborhood Black Hole Power Plant
You have probably never thought about black holes as a way to manufacture clean energy. This is either because you’ve never stared at the giant plasma jets shooting out of their sides and thought “gee, I wish I had one of those in my garage,” or if you have, because common sense prevailed and you realized that there is no way local zoning codes would allow that.
But it turns out that the laws of physics allow some pretty interesting things.
A common misconception about black holes is that they have much more gravity than other objects. After all, we always think about them sucking things in with so much force that light can’t escape; doesn’t that mean that they must have tremendously strong gravity?
You can spot the flaw in this argument by imagining crushing the Earth. You may remember that Newton discovered that the force of gravity decreases with the square of the distance, so that if you move twice as far away from an object, you’ll feel a quarter of the force. It’s also proportional to the mass of the object, so twice as heavy, twice as much gravity.
Right now, you’re (probably) sitting somewhere between 3,950 and 3,970 miles from the center of the Earth. (Depending on if you’re at the North Pole, the Equator, or on an airplane) If you moved 250 miles up to join the International Space Station, you’d be about 4,200 miles from the center, and gravity would be about (3,950/4,200)² times weaker, or about 90% of what you’re feeling now. (Important fact: the ISS doesn’t stay up because it’s beyond the reach of gravity; it stays up because it’s moving fast enough that it keeps missing the Earth as it falls.)
Now, imagine that someone suddenly crushed the Earth so that it was half its current size, but left you right where you were. What would that do to the force of gravity on you? Nothing: there’s still the same amount of mass beneath you, and you’re still the same distance from its center. The only difference is that now nothing would be holding you up, so you would start falling.
Once you fell to the new surface of the Earth, you would be only half as far from its center, which means gravity would go up by a factor of four. But that’s not because Earth’s gravity is stronger; it’s because you’re closer.
(Strictly speaking, Earth’s gravity does get stronger than it was at that same radius before the Earth got crushed. That’s because, if you were somehow 2,000 miles from the center of the Earth right now, there would only be 2,000 miles worth of Earth under you trying to exert gravity. If the Earth were the same density all the way through, then a ball of half the radius would only have 1/8 as much matter in it, and so even though you were twice as close — and so getting 4x the gravity — on the whole you’d only feel half as much gravity as you are now. Of course, you’d also be buried 2,000 miles under the surface of the Earth, and so the strength of gravity would probably be the least of your concerns.)
But there’s a way to prevent falling: be in orbit. Let’s say you started out aboard the ISS, a steady 4,200 miles from the center of the Earth. Now, if the Earth got crushed, the gravity you felt would stay the same, and so your orbit wouldn’t change; you’d just see one hell of a show out the window.
That’s how things keep going: you keep crushing the Earth, and the amount of gravity someone on the ISS feels stays exactly the same. The only difference is that it’s now possible to fall closer to the center without running into the ground, and as you get closer, gravity gets stronger at that point.
When the size of the Earth reaches a certain critical size called the Schwarzschild Radius (about 1.5*10⁻²⁷ meters per kilogram of mass, so for the Earth, to about the size of a dime) the gravity at the surface becomes so strong that light can’t escape. But even at this point, the people on the ISS aren’t seeing any difference.
This has a lot of important applications if you’re planning on keeping miniature black holes around. It turns out that a mini black hole would be incredibly useful for all sorts of things. For example, when matter falls towards a black hole off-center (like gases from a star spiraling into a black hole), it rotates on its way in, and starts spinning faster and faster. Close to where it falls in, the rotational shear is enough to strip electrons right off their atoms — and when you accelerate charged particles like electrons or ionized atoms, as they accelerate when they’re spinning in a tight circle, they give off light!
Light produced by charged particles going around in a circle is called synchrotron radiation, after the most common way we make it on Earth, and it can be quite powerful. This light heats up the incoming gas, and (although we haven’t worked out the exact dynamics of how it works yet), the result is that two very powerful jets of plasma are shot outward along the axis of the black hole. This isn’t a violation of the laws of physics; the energy for these jets is drained straight from the gravitational field, i.e. the mass of the black hole, being converted directly into energy. Nor did anything escape the black hole; all of this happens to things before they fall in to it.
How do we know that these jets are real? Because in astrophysical black holes, they’re not only visible, they’re dramatic. The largest jet observed inside the Milky Way is from the black hole IGR J11014–6103 (don’t you love the romantic names we give them?), and it’s a 37-light-year-long death ray of plasma flying at 80% of the speed of light. You can’t see it with the naked eye; at those energies, all the light it emits is X-rays. A planet flying through its path would, shall we say, have a very bad day.
The jets from the supermassive black holes at the centers of galaxies are far bigger; they can reach thousands of light years. This is what the jet from the galaxy M87 looks like; the beam you see (as photographed by the Hubble Space Telescope) is 4,900 light-years long, and is one of the brightest radio sources in the sky.
Now, if we happened to have a miniature black hole, this would be awfully convenient. Say you dug up Texas to a depth of about forty meters. Assuming it’s mostly dirt, that would give you a mass of about 3.4*10¹⁶ kg, which you could compress into a black hole roughly the size of a Hydrogen atom. (We’ll leave aside the question of just how you would do that for a moment) Black holes are nicer than ordinary crushed objects, since by the time they’re that crushed, gravity has overcome any natural tendency they may have to spring back on you unexpectedly.
Why Texas? Because if you used a smaller state, you’d have to dig that much deeper to get enough matter, and that might make the whole project impractical. You’d have to excavate Connecticut a good 2km deep!
What’s nice and convenient about this is that if you’re standing a good distance away from it, say ten kilometers, the total gravitational pull you would feel from it is about five thousandths of a g, the acceleration you would feel in a car going from zero to 60mph in about 9 minutes. Not a problem. But if you got very close to it, say ten nanometers, you would experience an acceleration so great that you really can’t use Newton’s formulas anymore, and you really need relativity. (I’m pretty sure those stop working long before you reach the 4.6*10²¹g’s Newton claims. It would actually be higher.)
[A]ll you would need to do is take a beam of atoms — any old atoms will do, you can use junk or radioactive waste or used politicians — and fire them just a little bit off-center at the black hole.
So all you would need to do is take a beam of atoms — any old atoms will do, you can use junk or radioactive waste or used politicians — and fire them just a little bit off-center at the black hole. Out both ends shoots a nice, bright plasma beam, which you can fire at a suitably distant tank of water, boil the water, and run a generator. Poof! You’ve got a power plant that uses literally anything as fuel and produces no waste!
You might ask, is it safe?
One pretty obvious risk is that the black hole might lose its moorings, fall through the floor, punch through the surface of the Earth, and destroy the planet.
Forget the cartoon drawings of the Earth being sucked in by a super-vacuum-cleaner; like we figured out before, the gravity from a black hole once you’re far away from it is exactly the same as the gravity from any other object of the same mass. But just because it could absorb an extra Texas or twenty without anybody noticing wouldn’t guarantee the Earth’s safety; things could get very close to that black hole and fall in, so the black hole would slowly keep sucking in matter. (On a slow drift inwards, it probably wouldn’t get enough off-axis impacts to create appreciable plasma jets) So it might gradually threaten the structural integrity of things. (I don’t know if anyone has actually done the math on this)
Speaking as an engineer, this seems like a textbook case of Unnecessary Risk, especially when there’s a relatively simple fix: stick it in orbit. It takes just as much energy to get out of orbit as it does to get into orbit, so it can’t fall down by accident any more than the Moon can.
Another risk is that black holes aren’t really “black;” they actually glow faintly by emitting Hawking radiation. I’m going to skip the rather complicated explanation of just what that is; what’s important is that the smaller a black hole is, the brighter it glows, which means it loses mass to this light faster, which means it gets smaller still… and so an astrophysical black hole is essentially completely black and this never matters, but a small black hole can become much smaller very rapidly. (Which is a polite way of saying “go boom”)
Fortunately, it’s easy to work out just how bright our Texas-sized black hole would be, and it turns out that its lifetime is considerably longer than the age of the Universe. And because Hawking radiation is the only thing that escapes black holes, this means we’re actually incredibly safe: there is basically no way you can cause a black hole to stop being a black hole.
Of course, we’ve skipped over a bit of a hard part: namely, how do you crush Texas down to the size of an atom?
This part is actually pretty tricky, and if I knew how to do it, I’d be sitting with Elon Musk right now planning how to get our hands on enough backhoes to start the digging.
But it turns out that string theory may give us a way to cheat. You see, in ordinary physics, Newton’s constant — the number which measures the power of gravity — is a constant. But in string theory, it isn’t; instead, there’s a kind of field called the “dilaton” which pervades the universe, and Newton’s constant is just a measure of how strong the dilaton field is. In fact, the strength of gravity is proportional to the exponential of the dilaton field, which means that increasing (or decreasing) the field strength by a constant amount would multiply the strength of gravity by a corresponding amount.
Now, imagine you had a dilaton factory. The reason you needed a Texas-sized lump of dirt in the first place was because you wanted the black hole to be conveniently large to work with. But if you can crank up the strength of gravity, you can get the same acceleration with a lot less mass. So instead, you could take an object small enough to be (a) safe and (b) relatively easy to crush until it’s fairly small, zap it with dilaton so that gravity in its vicinity became stronger, and as long as you kept the dilaton generator going, it would stay a black hole, and you could mine it for energy.
You could still come out ahead on this: the energy you’re mining comes out of the mass of whatever you turned in to a black hole, plus whatever you throw into it later, so if it’s big enough it will still work. (I haven’t run the detailed numbers here)
There’s a new safety issue, though: if the dilaton generator ever breaks, gravity would fairly quickly return to its previous value. You’d still have a black hole, but now the Hawking radiation would get a lot brighter (because it’s really too small to be a stable black hole) and, depending on just how small your black hole was, it might explode. But you can still be cautious: if you used about 150,000 tons of mass (still not trivial to crush, but easier than Texas) then you would still have a full ten years to get the dilaton generator going again before anything exploded. Doubling that would give you nearly a century, which ought to be enough for anybody.
Dilaton generators would be pretty neat for other reasons. If you turn down the force of gravity, you have literally got an antigravity machine, which could be useful for any number of things, like lifting things or carrying them. (But sorry: it would get you into space easily enough, but it wouldn’t get you into orbit, because orbit is fast, not high)
Just one final catch: How do you generate dilatons?
This is the tricky part. In string theory, it seems that the best reaction for generating dilatons involves bouncing various things in a particle accelerator off another particle called a “D0-brane.” (Pronounced “dee-zero-brain”) Unfortunately, there’s no particularly easy way to make D0-branes, and because they’re very heavy as particles go, that’s a pretty serious engineering problem.
If we could solve that, we might be able to build a dilaton generator, and then build a clean power plant without having to crush all of Texas.
Alas. If I only had a brane.
