Could black holes be a better source of energy than stars?

Question

In my story, set in the far(ish) future, humanity discovers a way to extract energy from black holes (perhaps via the Penrose process?), which sparks conflict as various factions attempt to take control over previously useless and dangerous but now suddenly valuable black holes. This energy is extremely valuable because warp drives for faster-than-light travel require massive amounts of power, which made them impractical before the proliferation of Penrose process power plants.

In order for this to make sense, black holes would have to be a better source of energy than whatever humanity was using before, which I assume would be Dyson spheres/rings/swarms/etc. gathering energy radiated from stars.

To see if this is plausible, I attempted to compare the energy output of a Penrose power plant vs a Dyson sphere around the sun.

According to the Wikipedia article about the Penrose process, up to 29% of a black hole's mass energy can be contained in its angular momentum. So, assuming a black hole with the mass of the sun (which I know is too small to become a black hole, but I wanted to compare apples to apples), the total amount of energy that can be harvested from it is $(0.29\cdot1.989\times10^{30})c^2 = 5.18\times10^{46}$ joules.

For comparison, the sun emits a total of $3.9\times10^{26}$ watts.² Over the 5 billion remaining years of the sun's life, assuming its energy output remains constant, it will emit a total of $(5,000,000,000\cdot60\cdot60\cdot24\cdot365)(3.9\times10^{26}) = 6.15\times10^{43}$ joules.

So the black hole has over 800 times as much energy to harvest! But the real question is, how quickly can that energy be harvested?

According to Wikipedia, an object's energy can be increased by up to 20.7% using the Penrose process. That means the equation for how much energy we can get from a given mass is $0.207mc^2$. So, the amount of mass we need to toss into the black hole per second to match the sun is $\frac{3.9\times10^{26}}{0.207c^2} = 2.1\times10^{10}$ kilograms per second. But only half of that mass actually falls into the black hole, the rest can be re-used. So only $1.05\times10^{10}$ kilograms are consumed each second.

How much mass is that? That's about 1.75 Great Pyramids of Giza every second. At that rate, the mass of the moon would be used in $\frac{7.3\times10^{22}}{1.05\times10^{10}} = 6.95\times10^{12}$ seconds, or about 220,000 years.

For the sun, it would be $\frac{1.989\times10^{30}}{1.05\times10^{10}} = 1.89\times10^{20}$ seconds, or a little under 6 trillion years.

Based on the math, it seems plausible. (Assuming you can toss stuff in fast enough.)

So my questions are:

• If a civilization is not advanced enough to harvest energy from black holes, are stars the best source of energy?
• If a civilization is advanced enough to harvest energy from black holes, are black holes the best source of energy?
• Is the Penrose process the best way to harvest energy from a black hole?

By "best" I mean produces usable energy the quickest. I know matter-antimatter annihilation would release energy extremely quickly, but you have to create the antimatter first, which uses a bunch of energy. (In my universe, humanity never figures out how to create antimatter efficiently enough to get a net gain of energy by annihilating it.)

Answer 1

If a civilization is not advanced enough to harvest energy from black holes, are stars the best source of energy?

Certainly not. There are quasars and pulsars and nova and heaven only knows what other sources of energy are out there. Quasars and blazars¹ may be a bit too rare to be practical. It's like always having to drive a 40 mile round trip to get gas in your tank. Pulsars produce a ton of energy and are more frequent. In the long run, suns may have the lowest collectible energy density, but they're so honking common that practicality wins out over efficiency.

In reality, your people would use a variety of sources. A passing quasar for a quick top-off would never be missed — but a star if you must 'cause it's right over there.

If a civilization is advanced enough to harvest energy from black holes, are black holes the best source of energy?

Ignoring the issue of practicality (which will always require multiple energy sources 'cause those folks on the rim are a long way out and that makes refueling very impractical), then quasars and blazars are still your best energy sources, but they're more rare than black holes.

OK, You really can't ignore practicality. If you're half-a-galaxy away from the nearest black hole it simply doesn't matter if you can harvest or not. You're not going to spend the time and energy just to obtain the better energy density. If it takes less time to sit by a star than to travel to a black hole, you'll park that beast in orbit and get a tan.

Is the Penrose process the best way to harvest energy from a black hole?

This is, frankly, an impossible question to answer. (And don't believe anyone who tells you otherwise. No one can prove that one theory is better than another.) The Penrose process is theoretical. Hawking radiation, first theorized in 1974 only saw the first light of proof in 2010. Who knows when the Penrose Process will be proven, if ever? What's the value of claiming one theoretical method is better than another? What happens if you write your story this year only to have the Penrose Process disproven next year? You see, the problem is, you're treating hypotheses and theories as if they're right. Maybe they are. Maybe they aren't.

I have a couple of favorite stories that are getting harder to read because the author depended on being too realistic, too "hard science," and the science changed. Some people are funny, they think what we "know" today (even when it's only just theorized) represents the end-all of knowledge. Knowledge changes, science changes, theories come and go. If you stick to today's proven facts, you're safe. But the more theoretical and unproven your story's critical science, the more likely the story won't stand the test of time.

That's the value of fiction. It's nearly impossible to disprove fiction (e.g., Star Trek transporters) and once the fiction becomes popular people start working toward making it work (e.g., Star Trek transporters). But take an actual theory that becomes disproven. Now your "history" is wrong and people will stop liking the story. Yuck.

Which is a fancy way of saying, have fun discovering whether or not your fictional society can harvest black holes, but when it comes to the actual science behind doing it, you might want to stick with "Lieutenant, open the collectors and start filling our reserves."

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¹ Please forgive me for forgetting the quasars and blazars are believed to be special cases of black holes. Mentioning them at this point in the text is improper as the OP was asking about "what if we can't harvest black holes?" If you can't harvest black holes, you can't harvest quasars and blazars, either. However, I didn't bother to rewrite the paragraph because I suspect y'all'll understand my point (and, having found a good reason to write "y'all'll," I couldn't pass it up). Cheers.

Answer 2

Black holes are very interesting, and can be farmed for energy, as well as used for other purposes. There are some theories that suggest a Black Hole's event horizon could serve as a sort of civilizational hard drive, for example.

The issue isn't if black holes are effective energy sources or not, but the logistics and infrastructure needed to use them. If you have to travel 30,000 light years to get to Sagittarius A* (the central black hole at the centre of the Milky Way Galaxy), and then disassemble dozens of stars to create the structures needed to surround and contain the black hole for energy extraction, then you have a very long project ahead of you, and your subcontractors will be busy for millennia.

Smaller black holes orbiting in the Galaxy itself will have similar, if smaller issues.

So in effect, you will have a situation similar to the builders of hydroelectric power systems: the best sites for dams and power stations might not be located very close to where your customers for power actually are. (For the purpose of the question, I'll handwave the need for the equivalent of high power transmission lines from the black holes to wherever the power is needed).

Unless you absolutely require power on this scale, it seems much more practical to simply build Dyson swarms around the ordinary stars and harvest the energy from there. This is often known as a K-2 civilization, and represents a fairly straightforward and accessible way to generate power o the scale needed for a galactic civilization.

Answer 3

(By coincidence I was finishing a section of my book dealing with mining black hole energy today)

Harvesting energy from stars is easy. But it turns out that the tech (Dyson spheres) you need for it allows harvesting energy from black hole accretion in a stationary way, and this can be very efficient.

No, the Penrose process is not the best real or theoretical method of energy harvesting.

More detail, and a suggestion for a theoretical but science-based cool way of tapping black holes:

The Penrose process extracts angular momentum from a rotating black hole. It is not an easy trick to pull off, but one can do it in various ways (particles, superradiance, matter-antimatter reactions producing pairs of gamma ray beams where one is sacrificed and the other picked up outside...). However, eventually the angular momentum will run out. It is not a renewable source, even though it is big.

The most efficient way we know can extract energy from matter and a black hole is accretion disks and jets, since we have observed them. Matter falling into an accretion disk is losing its potential energy as it spirals in, radiating it away. We have good reason to think that the mass-energy conversion efficiency is up to 5.72% for stationary black holes and up to 42.3% (!) for rotating black holes (neutron stars give about 23%). By comparison, fusion is just 0.075%, and stars worse. That energy can be collected using a Dyson sphere (a fairly standard one, if high temperature, for a stellar mass black hole; a very big 1000 AU one for galactic black holes - as you get close to the Eddington luminosity I recommend carbon-tungsten statites or the alloys related to Ta$_4$HfC$_5$).

But there is more! The accretion process produces jets that can be about as luminous as the the disk itself thanks to complex electromagnetic effects in the swirling plasma. This is basically a Penrose process but electromagnetic (the Blandford–Znajek process), and possible to replenish by adding matter with angular momentum to the disk. That energy can also be collected using suitable megascale engineering (think giant coils).

Catching gravitational radiation looks very hard (weak coupling to matter), even though up to 1/8 of the masses of merging black holes are emitted in one burst.

Here is the thing that might make the story/worldbuilding fun:

Hawking radiation is a mere trickle, and mostly of interest for far, far future civilisations when the universe becomes cold enough. However, it can be boosted! In this paper, Frolov and Fursaev show that if you dangle cosmic strings nearly onto the event horizon of a black hole each string will emit about the same amount of Hawking radiation as the entire hole. For the right kind of thin strings this can boost the hole output by $10^{31}$ - enough to make a solar mass black hole produce 900 Watt, and smaller ones far more. Of course, solar-mass black holes are about the lightest that can form today, so you need to seek out the rarer primordial black holes that formed during the Big Bang.

So my suggestion is that a recent discovery of a way of making cosmic strings (cool objects on their own) enables tapping primordial black holes, triggering a rush.

Answer 4

1. An insufficiently advanced society such as our own Class 1 society may want to consider research into the harvesting of vacuum energy as one scientist hypothesized that the amount of usable energy in the volume of a coffee cup might be enough to boil an ocean and that would see to be a good starting point for harnessing large amounts of usable energy

2. A sufficiently advanced society perhaps classified as a Class 2 society should have other alternatives beside black holes including more common cosmological events like neutron stars and quasars

3. As has been suggested by others, there may not be sufficient data to determine whether the Penrose process could achieve your goal but the name sounds good if you're looking to give your process a title.

Answer 5

In my story, set in the far(ish) future, humanity discovers a way to extract energy from black holes (perhaps via the Penrose process?), which sparks conflict as various factions attempt to take control over previously useless and dangerous but now suddenly valuable black holes

Black holes have a significant problem -- availability. And to be able to use the Penrose process, a black hole is not enough - it must be a Kerr black hole, one with angular momentum that you can harvest.

There is another possibility, harvesting Hawking radiation. If the theory is correct, a black hole radiates energy at the expense of its mass; the smaller the black hole, the faster it radiates, so that below a certain size a black hole starts evaporating faster and faster until it disappears in a flash of gamma radiations.

The equilibrium temperature of a Schwarzschild black hole is 6.169 10^-8 times the ratio between the standard Solar mass and the black hole mass.

Also, emitted power is inversely proportional to the square of the mass, and a Sun-sized black hole would radiate 9 10^-29 W. Suppose we want one thousand gigawatts of power, or 10¹² W; if my calculations are correct, we need a mass of 1.8E+10 kg (18 million tons), which would radiate at a temperature of about seven billion K degrees - enough to photodisintegrate matter - and evaporate in 1.5 microseconds.

If a civilization could harness such a monster, you would have an incredibly compact form of energy, reasonably portable, which would continuously consume matter converting it into energy (and if the reaction got out of control, you would get an explosion of one jillion megatons when eighteen million tons of mass get converted to energy in less than two microseconds). Harvesting that energy would require very advanced technology, the black hole equivalent of betavoltaics. Perhaps clastovoltaics, from the Greek word κλάστης "to break".

But how do you create a multimillion-ton black hole keeping it stable in the process? The safest way would be to start from a larger black hole and destabilize it by feeding it with antimatter. You don't need to bring them all the way down to twenty million tons - just start the evaporation process until it has reached a sufficient speed, then wait a suitable number of years while preventing the black hole from absorbing ordinary matter.

Now, stable micro black holes (the size of the Moon) would become a sought-after resource: you need to locate them, electrically charge them enough to be able to tow them (somehow!) near some other huge source of energy suitable for the production of antimatter, and convert them to matter-annihilation power cores.

Especially during the initial slow cooking period, when someone else has paid the huge location, towage and antimatter priming costs, and the black holes have started giving off mere microwatts of power but are still a long away from becoming difficult to control, it would make economic sense to try and steal them.

But to answer your question: would that be a better energy source than a star? It depends. Energy density is way higher, and it's far more portable and efficient. On the other hand, a star is not usually a few microseconds away from blowing you and everything else in a radius of several million kilometers to smithereens.

Answer 6

If a civilization is not advanced enough to harvest energy from black holes, are stars the best source of energy?

You would be hard-pressed to find a better source than stars, if you can't use black holes. The only thing harvestable by that civilization that is bigger/has more energy than a star is a group of large stars.

If a civilization is advanced enough to harvest energy from black holes, are black holes the best source of energy?

The problem with harvesting from black holes's momentum lies in how practical it is. One mistake and your equipment becomes impossible to recover/repair.

A safer bet would be to harvest from the accretion disc around a supermassive black hole. Those discs have temperatures in the order of millions of degrees an can be more massive than the biggest stars. TON 618 is a black hole of 66 billion solar masses, whose accretion disc outshines its galaxy - imagine the mass and energy of that disc.

Is the Penrose process the best way to harvest energy from a black hole?

As you mentioned, that process can take up to 29% of the black hole's mass-energy. Absorbing its Hawkings radiation will eventually net 100% of its mass energy, but will take prohibitively, exponentially more time - taking all of the momentum energy may get you done well past the heat death of the universe, but even that would be only a fraction of the time needed to extract the whole energy-masss of the hole through Hawkings. So Penrose is still the more productive way to go.

Answer 7

Theoretically, just dropping mass into a rotating black hole will release more energy than the Penrose process, since the mass-energy conversion has an efficiency of 42%, compared to 0.7% in nuclear fusion. 1. Based on our current knowledge, yes. There are many Dyson superstructures designed to leech the energy from a star. And the energy is sufficient for just about anything a civ that advanced can dream up. 2. Technically, yes, but here's the elephant in the room. Black holes aren't exactly safe. One tiny slipup, and you've got a seriously scaled-up Chernobyl. Equipment worth gazillions of currency units, gone in a flash. 3. Read the first paragraph.