Black Hole Engineering
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Ah, black holes. Flaws in the fabric of the universe. Empty voids from which nothing can return. The ultimate unknowable mystery.
But what are they good for?
Basics
Lets start with a brief introduction to black holes.
Things like planets and stars and other massive bodies have gravitational fields around them that tend to draw things toward them and trap stuff on them. In order to get away from such a body, you need to shoot yourself off it with a speed higher than its escape velocity. If you don't have that much speed, you can't get away. When you pack enough mass into a small enough volume, its gravity gets so high that the escape velocity is higher than the speed of light. Because nothing can go faster than light, nothing can escape. This is a black hole.
That's the description motivated by Newtonian gravity, anyway. But when gravity gets really strong Newtonian gravity breaks down and you need to use general relativity instead. Curiously, the size and mass where light (and everything else) is trapped is the same as the Newtonian case. But instead of light and other things flying out, looping around, and coming back space-time gets strange. At the critical distance where light would be trapped you get a surface called an event horizon. Nothing that passes into an event horizon can ever get back out again. The gravity at and inside the event horizon is so strong that it rotates space and time enough that the direction inwards toward the center becomes your inevitable future. You can no more resist going toward the middle of the hole that you can avoid seeing what fate awaits you.
An uncharged and non-rotating black hole at rest is described by the Schwarzschild geometry. The radius of its event horizon is the Schwarzschild radius
rS = 2 G M / c2
where M is the mass of the black hole, G is the gravitational constant, and c is the speed of light in vacuum.
Charged and/or rotating black holes get more complicated.
Energy
Famously, noting that goes into a black hole can ever come back out again. But something comes out. For it turns out that black holes have a temperature and that, like everything with a temperature, they radiate electromagnetic radiation. In fact, being perfectly black, they radiate as a perfect black body. This radiation is called Hawking radiation after its discoverer, physicist Stephen Hawking. For normal sized black holes, those the size of stars or galaxies, this temperature is very small and the radiation power is absolutely minuscule. But the smaller the hole, the hotter it gets and the more power it radiates. For a black hole with mass M, the Hawking temperature Th is
Th = ℏ c3 / (8 π G kb M)
where ℏ is Planck's constant, π is the circle constant, and kb is Boltzmann's constant. Curiously, this means that the wavelengths around the peak emission of light in its spectrum is near the size of its event horizon. The power radiated by a hole of this temperature is
Ph = ℏ c6 / (15360 π (G M)3).
The radiated energy comes from the black hole's mass-energy, so a black hole will shrink over time as its mass is radiated away. As the mass decreases, the temperature goes up and so does the power output. So you get a runaway process of the hole getting hotter and hotter and radiating more and more power until POOF! It's gone in a flash of light and radiation. The lifetime remaining of any black hole, assuming more mass doesn't fall into it, is
th = 5120 π G2 M3 / (ℏ c4).
This is a neat result. It allows perfect conversion of mass-energy into radiant energy. However, the actual implementation can get a bit inconvenient.
Let's skip for the moment the details of how you get a black hole. We'll assume that you have a magic black hole making box that can pop out whatever size of hole you need. Now let's say you want a megawatt of power. What size of hole do you need? It turns out to be a cool 18.8 billion metric tons. A hole that size is rather hard to carry around with you. And its temperature will be 6.5 billion kelvin. At that temperature its radiation is primarily hard x-rays and gamma rays. On the plus side, it's about 3000 times smaller in radius than a typical atom. So you could slip it into your pocket; just don't expect it to stay there.
Here we see one of the issues on trying to utilize Hawking power from black holes. Usable amounts of power generally come with horrendous power to mass ratios with the energy released as highly penetrating ionizing radiation.