A Dyson sphere around a black hole

Better link: https://arxiv.org/abs/2106.15181

The results are fairly obvious: CMB and Hawking radiation provide almost zero power output, while an accretion disk and relativistic jets can provide a lot of power.

Oh cool, CC-BY!

In theory you can get an arbitrary amount of power from Hawking radiation if you have a lot of very small black holes instead of just one big one. I feel like the stability of the negative-feedback control systems for their orbits might be important here, especially if they're orbiting something you care about like your home planet.

As far as I understand, small black holes could be used as a super efficient energy storage („Kugelblitz“), but hardly as a source, assuming that primordial black holes are rare. Primordial black holes afaik are the only theorized origin of a sub stellar mass black hole at this stage of the universe‘s timeline.

How would you tap an accretion disk? How would you tap relativistic jets?

If only there was a way to break up the smallest size of black holes (there isn’t). If it was split up into several or thousands of much smaller black holes they, being much smaller would give off energy faster.

Energy is energy wouldn’t a matter black hole and an anti matter black hole just make a black twice the size, minus a bit for gravity waves.

I was thinking given a large enough gravity wave it might be able to stretch a black hole apart. How huge that could be, and how that could be generated is probably beyond the limits of reality.

Solar panels?

Yeah, making tiny black holes could be pretty challenging, but I feel like it's just an engineering challenge. Is there a fundamental reason I'm missing that you can't just build a really precise, solar-system-scale particle accelerator to slam together a lot of mass into a tiny space to make tiny black holes?

I don’t like the idea of having a black hole of any size in my solar system.

It’s just too much mass in too little space. It’s essentially the same requirement as fusion, but almost infinitely more difficult.

If you could make a fusion reactor almost infinitely better then it would produce a black hole which would immediately evaporate releasing more energy than you could ever imagine - but no way it can be done.

I have bad news for you:

https://arxiv.org/abs/1909.11090

this would easily be the most awesome discovery of the last 50 years if it turned out true and we could locate and study it...

And so NIMSSyism began...

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.

Hawking radiation propulsion has the perfect specific impulse: exhaust velocity is the speed of light. Black hole hawking radiation also is perfectly efficient: 100% of the mass is converted into energy. D-T fusion only converts 0.4% of the mass to energy.

There are many awful engineering problems of a black hole drive, but they're not so bad as to dismiss out of hand. See https://arxiv.org/abs/0908.1803v1

How about a big ol' waterwheel?

Kurtzgesagt made a video explaining some possibilities. In short, you can throw mass or radiation at a spinning black hole and "steal" rotational energy from it.

https://www.youtube.com/watch?v=ulCdoCfw-bY

Heat water to produce steam, use steam to turn turbine. :P

The energy requirements to make a useful one are ..well.. astronomical. One interesting concept is to build a dyson swarm out of Mercury [1]. No, not the element, Mercury the entire planet. Then use that swarm to generate Kugelblitzes for interstellar travel.

[1] https://www.youtube.com/watch?v=jW55cViXu6s

Oh, you wouldn't want to be able to split up black holes, since that means they could be destroyed during warfare.

Depending on what the cosmological constant is, massive black holes could be quite useful in the far future. 10^100 years from now, long after all the stars have gone out, it could be the case that the only life in the universe would be huddled up against the event horizon of supermassive black holes, exploiting the tiny temperature difference between the pseudosurface and the void to generate a trickle of power.

Splitting black holes would rob the far future of that power source to be used now. You could do it, but why shorten the useful life of the universe?

also, you can use light, instead of matter.

Termed the "halo drive", it's a very nice theoretical concept: https://www.youtube.com/watch?v=rFqL9CkNxXw

Only 50?

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.

You know, if you asked Christiaan Huygens in 01671 about the possibility of detecting a 4-km-long tunnel getting shorter by a factor of one in a sextillion for a hundredth of a second, he surely would have doubted that it was possible. But it's only been 350 years, and when LIGO detected its first gravitational waves five years ago, that's precisely how it did it.

By contrast, there's ample reason to believe that black-hole power plants are possible. In fact, the spatial precision required is actually the same order of magnitude as that of LIGO, about an attometer. So we might not even have to wait 350 years for it.

steampunk had it right

Like many things, they'll be located a few short AU's beyond the reach of your star system's Zoning Board. Maybe that vacant orbit right next to the antimatter battery factory?

Well, in some sense, black holes are the least interesting objects in the universe - they are entirely characterized by their mass and angular velocity (possibly charge as well?).

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.

If ring singularities exist then smushing two together at right angles could fling singularity droplets out.

They are the least interesting objects outside. It is quite possible that inside they are much more complex than a hypothetical singularity.

>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.

Depends on the universe.

Let's use your parenthetical as an excuse to keep charge vanishingly small, because we can avoid thinking "Which charge? Which charge carrier or carriers? What's the distribution of charges?", and largely ignore the electro- effects of electrovacuum (which answers these, but in surprising ways when you look deeply).

In a chargeless vacuum Schwarzschild or Kerr universe, we have total coordinate freedom because there is nothing there but the mass at an infintesimally small point, p. If one builds a system of coordinates with p always at a single spacelike point (say, the spacelike origin), then the symmetries of this vacuum system let one chop away spatial position (e.g. const.coord.x, const.coord.y, const.coord.z, t -> 0,0,0,t) and consequently the vector-quantity linear momenta of the black hole vanish. Moreover, these vacuum spacetimes are also eternal (the black holes do not grow or shrink), so we can do t = const. too. With suitable coordinates, gives us two free parameters: mass & spin (and in Schwarzschild, just one: mass).

These solutions do not superpose additively. By the Raychaudhuri focusing theorem, if we add a point mass to the Schwarzschild black hole universe, the two masses will eventually collide. We have broken the spherical symmetry of the Schwarzschild solution, and when we solve the geodesic equations, we find caustics, where our two infinitesimal masses can be in the same infinitesimal space. We have also broken time symmetry: at past time the two masses are spacelike separated. In the future they are not, as they will merge into one black hole. We also have the problem that the black holes move with respect to one another, so we either adapt or system of coordinates to be comoving with the black holes, or we have one or both of them move against the spatial-coordinate part of our system of coordinates.

When we take this further by breaking other symmetries than the time one, e.g. by adding angular momentum to the system, we have to consider the evolution of orbital angular momentum of the pair, and possibly the spin angular momentum of each. Either of our previous-paragraph choices with respect to encoding the coordinate evolution of the spatial distance between the pair of black holes complicates the calculation of the related vector quantities.

We're still in the land of a small number of parameters, but have gone from the three time-independent [mass, spin, charge] to eleven time-dependent [mass, spin, charge, 4-location, 4-linear momentum].

We can explode the number of parameters though by returning to "what is charge?", and equipping these universes with fields of matter. At this point one runs right into the question of: "does the no-hair conjecture hold in a physically plausible universe surrounding a theoretical black hole?" or almost equivalently "when do theoretical black holes fail to approximate astrophysical black holes?", and Ligo/Virgo are good laboratories for studying whether merging black holes go completely bald.

(The hair that is supposed to bald away may be soft and indirect: the circulation of gas and dust at a distance may reveal that a given black hole was previously more than one black hole. After merger, none of that should make a difference to anything (including a 3rd black hole) falling into the balded merged black hole that the merged black hole was previously two black holes. More critically, in the enormously distant future, the evaporation of the merged black hole should not reveal the number or types of objects that fell into it during its history, whether those are black holes or some neutral mix of standard model particles. The Hawking radiation spectrum at any moment should depend only on the eleven parameters in the previous paragraph. But maybe that still-outside dust and gas has memory that remains relevant arbitrarily far into the future. Or maybe classical general relativity is wrong and rather than being crushed into a memoryless ultramicroscopic point, the ingested gas, dust and other black holes retain or at least reveal their individual identities even during evaporation).

Questions like these make black holes extremely interesting, I think.

It's possible, but as long as that stuff stays inside, we have no reason to care (or even tell) whether "inside they are much more complex than a hypothetical singularity".

The central theoretical problem is that taking Hawking seriously, the stuff inside stays inside, but inside goes away. What happens to the stuff? There are more theoretical answers to that written down than there are actual theorists, and presently no astronomical or laboratory observations which let us throw practically any of them away.

(Also of course, inside might not go away after all -- not at all or not completely -- with large numbers of explanations of how that might work, and nothing concretely observed that lets us discount such possibilities in favour of total evaporation.)

maybe more than that, but I‘d say various discoveries during the golden age of physics would be contenders. Quantum effects, SRT & GRT, nuclear energy, among others. Black holes are just one interesting phenomenon of nature, albeit a pretty fundamental one.

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.

I'm pretty sure you're referencing this video: https://www.youtube.com/watch?v=Qam5BkXIEhQ

But on the off-chance you're not - and for everyone else who's intrigued by this comment's concepts - I can recommend watching it.

> 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.