Containing a Black Hole's End-Of-Life

Question

Let's set the scene. Some advanced civilisation has taken to creating artificial Black Holes and using them as commonplace batteries - without the intention of refueling them. They simply hollow out planets and put bigger black holes in there to make reactors, instead!

Assuming we're not being completely flippant with throwing around black holes willy nilly, one can imagine a large shielded casing with reflective mirroring or an electromagnetic cage inside, into which a hose or plug can be connected to fire a particle stream or laser to create a Kugelblitz using an initial power surge, which the battery then contains, and can be then plugged into whatever needs power.

These are probably not your AAAs, more like car batteries, (or in this case, weapon, ship or even city batteries). Big, clunky industrial blocks that are likely in the kiloton to megaton range, mass-produced (at least as far as they're in demand), and maybe offset with some handwavium gravitic shielding so they can be a little smaller and not create gravitational distortions.

They'd still be bulky and heavy (the most effective radiation shielding is a thick wall of matter, after all), but the idea being they're transportable and versatile and can charge power-hungry equipment where wired connections won't do.

Unless I've horribly misunderstood something somewhere, black holes will eventually evaporate, and as they do, their energy output will inversely be increased, and in their last second of life, they'll release a huge amount of energy within the span of a second.

Because quantum physics is hard and we still don't know enough about how black holes work, I'm gonna say for the purposes of this thought experiment that it will likely end in a gamma-ray burst, or about an explosion roughly equal to 10^28 megatons, comparable to a Type Ia supernova.

If these are being used as generic batteries, and this civilisation presumably doesn't want to be put off by random supernovae going off because the ship's engineer got drunk one night and forgot to refill the tank, how might they go about designing a battery that could withstand or even potentially harness a black hole's evaporation followed by a gamma-ray burst?

Answer 1

TL;DR:

• you can't hold on to uncharged black holes
• big black holes are too heavy and too low power output to easily use as batteries
• small black holes can't easily be charged

therefore

• you don't have to worry about confining the final moments of a black hole, because you won't be able to confine a black hole of any size in the first place.

There are other issues with your scenario, but I think BenRW has them covered.

Black holes make for terrible batteries.

---

There are a whole bunch of issues with using black holes as mere batteries.

Lets firstly assuming that Hawking was correct about black hole radiation and mass loss. There are some useful equations on wikipedia under black hole evaporation, but the main ones to care about are:

• the lifetime of a black hole is proportional to the cube of its mass. If black hole A is 10 times heavier than black hole B, then it will last 1000 longer.
• the power output of a black hole is inversely proportional to the square of its mass. If black hole B is a tenth of the mass of black hole A, then its power output will be 100 times greater.
• the schwarzschild radius of a black hole is proportional to its mass.

This means that the rate of power output and hence mass loss accelerates, which in turn means that it doesn't get really interesting til it gets quite small, at which point it is a bit too interesting.

In order to "recharge" a black hole battery, you have to pump mass or energy through the event horizon. When your black hole becomes smaller than ~2 fm across, this becomes a wee bit challenging because it starts getting too small to fit protons and neutrons into it. This happens at a mass of $M = {c^2r_s \over 2G}$ (where $r_s$ is the Schwarzschild radius of the hole and $G$ is the gravitational constant) or well over a billion tonnes.

This very-hard-to-recharge billion tonne battery only has a power output of 200 MW or so, which doesn't compare well with the same mass in, say, space-based solar power systems, or geothermal power, or even regular nuclear reactors. Smaller holes produce much more power (356 TW for a million-tonner), but suddenly you can't fit matter into them and instead the infrastructure required to recharge them looks like multi-terawatt or petawatt gamma-ray lasers which are a) hard to build b) probably highly inefficient, requiring many more petawatts of input power in order to function. Obviously if you can make kugelblitzes in the first place then you probably have suitable infrastucture, but "being able to wrangle a stupendously powerful gamma ray laser array to shoot somewhere" is not the same as focussing it on a particular subatomic black hole that you might not be able to hold on to and that is very hot and radiating exotic stuff back at you. That's a much more challenging bit of shooting.

The second problem is holding that billion tonnes of subatomic-scale stuff in one place. You can't just grab onto it. If it is in a gravity well like a planet, then it'll start falling towards it. It probably won't threaten the planet much (because a hard-to-recharge black hole can't eat matter at a problematic rate, which is why it is hard to recharge). If it were big enough to inject a load of protons or electrons into you could give it a net charge you might be able to hold it up electromagnetically, but it would need to have a stupendously high charge to be able to support its own weight, and such an object is a) incredibly hard to charge in the first place because of coulomb repulsion (its own charge repels the incoming ions), and b) inclined to neutralize its own charge by sucking oppositely-charged ions out of matter around it. A tiny black hole couldn't eat those ions, but you also couldn't charge it in the first place, which is awkward.

"Oh, I could charge it up in deep space and then let it shrink to below the size where it can't eat ions" you might think. The evaporation timescale of a billion tonne black hole is a good trillion years. You'll need to be patient, and there's still dust and gas in deep space.

"Okay, I'll just make a kugelblitz of a more manageable size and useful power output" great! But now you can't give it a net electrical charge, which means you can't hold onto it, which means it'll immediately fall into your planet and go foom deep below at some point in the future and possibly distress seismologists. Remember you can't get more mass-energy out of a black hole than it contained in the first place. A million tonne black hole will release 10²⁶ joules during its evaporation, but that'll be stretched over ~2500 years which makes it not-exactly-Earth-shattering and gives you a little while to evacuate if you felt the need. It'll release ~6.6x10²⁴ J in its final year (which coincidentally is about the same amount of energy that the Sun delivers to the Earth over a year), and ~2x10²² joules in the final second, but there's a lot of mass to spread all that energy over.

As I said above... black holes make for terrible batteries.

If you want to generate power from them, you want much larger ones and just soak up energy radiating from their accretion discs and polar jets (this can be surprisingly efficient, but requires quite a lot of matter to fuel the process). If you have a nice rotating black hole, you could use the Penrose process or the Blandford-Znajek process. Any of these approaches has a lot more in common with Kardashev 2+ stellar-scale engineering than batteries.

Answer 2

Realistically, you can't.

But this is sci-fi, and that you're already using Clark-tech (indistinguishable from magic) in the premise — I will get to why in a moment — so just use the answer that Star Trek script writers gave when asked how the Heisenberg compensator works ("very well, thanks").

Black holes do indeed evaporate. For stellar objects, even mountain-mass objects, this takes ages, but for the mass range you're talking about, it's hardly any time at all:

$$\tau_{\rm evaporation} \sim \left( \frac{M_{\rm black~hole}}{M_\odot}\right)^3 \times 10^{66} {\rm ~years}$$

— https://astronomy.stackexchange.com/questions/41004/calculating-the-black-hole-evaporation-time

For a 1 kg object (~ car battery), it evaporates in 4e-18 seconds; For a 1 kiloton object, 3 seconds; for a 1 megaton object, 95 years: https://www.wolframalpha.com/input?i=%281kg+%2F+mass+sun%29%5E3+*+1e66+years

The explosion is still bound by $E=mc^2$, so none of these will look like a Type Ia supernova — fortunately, because if they did, the planet would explode faster than the special effect used for Alderaan in Star Wars.

But, under currently known physics, the power output is not under your control, it's an inherent property of the interaction of quantum mechanics with a curved space, and the black hole constantly gets smaller and brighter as time passes, no matter what you do — so you need Clarktech to change that into a battery that only emits power when you want it to.

I'd suggest a slow-time field, as black holes already do something a bit like that. Also you say you want gravity shielding anyway, and in relativity there's a strong connection between time dilation and gravity.

But with current tech, there's even worse problems, as you also need Clarktech to be able to use the power output at all. Why? Because the power output is a thermal spectrum; for a heavy-dim-cold black hole, it's safe but useless.

Unfortunately, by this I mean:

To get down to photons that “only” photo-ionise normal matter (about 6eV), you need a black body to be “only” about 70,000 K. That in turn means the black hole is now about 1766 trillion tons, and has a power output of 114 microwatts.

— https://benwheatley.github.io/blog/2022/05/14-17.06.59.html

For a megaton, the power output (luminosity) is 3.6e14 watts, and the temperature is 1.23e14 K which corresponds to a peak of 4.15e10 eV, which is the kind of ridiculous combination that may lead to Randall Munroe writing a book about how to get a fatal dose of radiation from Higgs particles.