A Dyson sphere around a black hole

Crane and Westmoreland looked into this: "Are Black Hole Starships Possible" (2009) https://arxiv.org/abs/0908.1803v1

A black hole is generated when mass-energy density is above a certain threshold. You need to pack about a megatonne of mass-energy in a sphere 3 attometers in diameter to get a black hole approaching a useful lifespan. You could do it with bosonic matter, but photons are easier. Well, "easier":

>In Section V below, we discuss the plausibility of creating SBHs with a very large spherically converging gamma ray laser. A radius of 1 attometer corresponds to the wavelength of a gamma ray with an energy of about 1.24 TeV. Since the wavelength of the Hawking radiation is 8π^2 times the radius of the BH, the Hawking temperature of a BH with this radius is on the order of 16 GeV, within the limit of what we could hope to achieve technologically.

>[...]

>In a previous paper by the first author [9], it was proposed that a SBH could be artificially created by firing a huge number of gamma rays from a spherically converging laser. The idea is to pack so much energy into such a small space that a BH will form. An advantage of using photons is that, since they are bosons, there is no Pauli exclusion principle to worry about. Although a laser powered black hole generator presents huge engineering challenges, the concept appears to be physically sound according to classical general relativity.

The process of aligning the laser array will be interesting, however. From Wikipedia:

>Unlike most objects, a black hole's temperature increases as it radiates away mass. The rate of temperature increase is exponential, with the most likely endpoint being the dissolution of the black hole in a violent burst of gamma rays. A complete description of this dissolution requires a model of quantum gravity, however, as it occurs when the black hole's mass approaches 1 Planck mass, when its radius will also approach two Planck lengths.

See table 2 from the paper. A 0.32 attometer wide black hole has a surface temperature of 98.1GeV and is losing 61.4 kilograms per second-- 5,519 petawatts of ultra-hard gamma radiation! Even at that diameter it has a sizable weight of 108,000 tonnes, but it doesn't have long to live-- a couple weeks. A poorly collimated laser array will produce undersize black holes which will rapidly evaporate. The paper suggests keeping them well away from Earth, on the other side of the Sun if possible. Not hard-- you'd want to put the array well within the orbit of Mercury for better solar power flux.

This is great, thanks! I hadn't thought about the Pauli exclusion principle problem, which I guess tells you how well I'd understood the problem. And of course I don't know anything about quantum gravity. I was thinking that, for use as a power plant, you want much larger black holes, not only bigger than a proton, but actually bigger than an atom, on the order of a nanometer, for two reasons: first, so that the gamma rays coming out are reasonably low energy (hundreds or thousands of electron volts instead of GeV); second, so that you can continue feeding it with regular baryons instead of keeping your spherically converging laser focused on it. But if you do that, you only get a tiny fraction of a watt out of it, and it's uselessly inefficient; even if you made trillions of these little black holes, the energy payback time of the project is measured in octillions of years if you're feeding useful photons into them.

So the sub-attometer-sized black holes described here seem like they might be a lot more practical than what I was thinking of. But... what does it take to stop TeV gamma rays? (And I guess they might also spew out strange matter and naked truth and the like, but you could probably just toss it back in.)

The billion-tonne gamma-ray laser they're talking about here is absolutely tiny.

They’d be more useful as an energy source for ships than as a power plant. You would make them in a solar system where lots of energy is available and use them to power a ship going to a different star system, one with no infrastructure of its own. Once you’ve arrived, you colonize and eventually build your own Dyson swarm to harvest the energy to make them yourself.

>don't know anything about quantum gravity

Nobody knows anything about quantum gravity, which is the problem ;)

>order of a nanometer

As db48x says, synthetic black holes aren't going to be much good as power plants, just because it's so darn hard to get them big enough that they can consume normal matter. Let's talk bare minimums. Say the nucleus of an hydrogen atom is about 2.4 femtometers wide. Plugging the numbers into https://www.vttoth.com/CMS/physics-notes/311-hawking-radiati... the mass of a black hole that size is 8.07991 * 10^8 metric tons. That is a lot of laser pulse power to get into a single point just to create the black hole. Wolfram alpha claims it's 2.01718 x 10^25 watthours. The sun radiates 3.828 x 10^26 watts, so we need about a tenth of total solar output for an hour-- assuming we can convert captured solar power into coherent gamma rays with no loss, which there is currently no plausible physical way to do, so we probably need 10 or 100 times as much power. We're beyond future ultratech, and getting into solar engineering.

Assuming the black hole is created, which is hard enough, we have further problems. A 2.4 femtometer black hole is still darn hot: it's radiating a total of 545.6 megawatts of light with a peak of 51.3 MeV-- still ultrahard gamma radiation. Our beam of hydrogen ions need to fight past this headwind and into the singularity-- quickly. It's losing 6.054 micrograms per second, which will be hard to deliver as a single row of hydrogen nuclei.

Making the black hole bigger in the first place will make it easier to feed... but if you can commandeer a tenth of the Sun's output at will, you don't exactly need domestic power from a black hole.

Isn't this rather theorized for interstellar travel anyways? If you can somehow funnel the output of this to push to one side and somehow keep a ship attached to it.. Well you'd reach a nice fraction of light speed.

> but you could probably just toss it back in.

The thing with very small black holes is that they're virtually impossible to feed stuff into - not only are they an extremely small target, but the flood of energy escaping will push away any matter that comes nearby.

Sure, that's easy enough to do: your ship consists of solar sails orbiting the black hole that spread out when they're on the nose side of the black hole, forming an opaque sphere that's incandescent on the inside, and fold when they're on the tail side, letting both the Hawking radiation and the incandescence shine past them. But being able to convert arbitrary matter to useful energy at 100% efficiency would be a pretty useful thing when you're not just beaming it into space, too. For example, it would make it straightforward to power your black-hole-building machine.

However, the trouble with larger black holes like the 2.4-femtometer example is not primarily that they require a lot of mass-energy to produce, but that they last a long time. According to the calculator linked above, it is indeed radiating 545.6 megawatts, which sounds like a lot. But compared to the 808 million tonnes you put into it, it's not very much; it will take you 4.2 trillion years to get back the energy you put in, about 250 times the current age of the universe. (The lifetime calculation on that page is shorter, only 777 billion years, because it's assuming you're allowing the black hole to evaporate rather than feeding it to keep it the same size.)

(BTW, actually that was all for a 2.4-femtometer-radius black hole, not a 2.4-femtometer-diameter one.)

This is really shitty energy-efficiency from a time-discounted perspective. If you use a conservative 3% yearly discount rate, the time-discounted earnings from your power plant over those 777 billion or 4.2 trillion years are equal to their non-time-discounted earnings over only the next 33.3 years. So from an economic point of view your efficiency is not 100%; it's 7.9e-10%, 0.000000000786% efficient. And that's not even taking into account the costs of building the giant gamma-ray laser.

So, for reasonable economic efficiency, you really need to build a black hole with a lifetime of 100 years or less. That means 400,000 tonnes or less, radius of 6.1e-10 nanometers (0.61 attometers) or less, 300 trillion kelvin or more, 102 GeV or more, 2.1 petawatts or more. In nuclear-bomb terms, that's 0.5 megatons per second (still very small compared to the sun's 390 yottawatts or 85 petatons per second), except that it's coming out in 102 GeV photons. That's about the mass of a silver atom, though still very small compared to the Oh-My-God Particle.

As skykooler points out, this could complicate the task of feeding the monster. Maybe you could set it to orbiting at a few kilometers per second inside a solid object such as Ceres, so that it occasionally gulps a proton on its way through the body, leaving a trail of rapidly cooling subterranean plasma in its wake.

Of course, if all the energy that's coming out has to go in through a nuclear gamma-ray laser, it's not really a power source, just a battery that's conveniently portable and has a built-in rocket engine.