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While it is popularly believed that black holes are like giant vacuum-cleaners in space, it is not actually completely true that anything that falls into a black hole is lost forever. In reality, black holes are actually the most powerful sources of energy in the universe, even more so than stars themselves. Even though black holes are famous for not allowing even light to escape, this is only true if light enters the event horizon: their accretion disks are capable of producing light as long as there's a constant source of matter feeding them. When matter falls into a black hole, tidal forces stretch and heat up the material to extremely hot temperatures which gives off potent x-rays. Supermassive black holes in particular, when fed a lot of matter, have the potential to outshine entire galaxies.
Even black holes themselves give off their own energy known as Hawking Radiation, which, in layman's terms, is the result of black holes slowly evaporating over inconceivably-long time scales of over 10^64 (that's 64 zeros) years on average due to quantum effects near the event horizon. A future space civilization is likely to take advantage of black holes around the tail end of the dying universe when there's no more stars to use.
Harder science fiction will typically rely on one or more of the following real-world theories:
Energy is released from matter as it falls into a black hole from the accretion disc. This can be captured and turned into useful forms.
Black holes have magnetic fields that can be harnessed to generate power.
Spinning black holes produce rotational energy that can be extracted.
Black holes that are not fed will slowly evaporate in the form of Hawking radiation, which could theoretically be captured. (In practice, the universe is not yet cool enough for this form of decay to be possible.)
A black hole can be used as a Reactionless Drive for a spacecraft by placing it in the intended direction of travel so that it pulls the ship along behind it.
Softer sci-fi tends to handwave it or cite technobabble such as The Power of the Void.
Of course, this is all dependent on a civilization having developed technology that can withstand the extreme conditions near the event horizon, which include massive gravitational and radiation effects and Time Dilation. Additionally, things typically will Go Horribly Wrong if the black hole breaks free of any confinement used (for example, if it's a microsingularity housed within a Space Station or Cool Starship), or the infrastructure that harvests energy is damaged and begins to fall in. In which case, this overlaps with Nature Is Not a Toy.
Compare Our Wormholes Are Different, Spaceship Slingshot Stunt, and Gravity Master for other ways black holes could be put to use.
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Star Trek Online: Most Romulan ships use a singularity core consisting of a confined microsingularity, instead of a matter-antimatter warp core. Playable Romulan ships are additionally able to manipulate the singularity for various technobabble effects. The "ship destruction" animation for Romulan ships has the ship collapse into its own drive singularity rather than merely exploding as with ships of other factions. Then it explodes.note This is probably to justify warbirds still causing damage to surrounding ships when they're destroyed (other ships go into a "warp core breach"), but black holes release their mass as energy when they evaporate.
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Transformers: Devastation: Sixshot boasts that he's powered by a hermetically sealed singularity when Optimus Prime first confronts him. Rather than intimidating Prime into surrendering, it instead motivates him to order the Autobots to disengage the power inhibitors on their weapons because they can't afford to worry about collateral damage when faced with such a powerful foe.
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 The Transformers Megaseries (Comic Book)
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Rocketship Voyager: On finding themselves on the other side of the galaxy, the crew of Voyager locate an alien space station orbiting a 'black star'. B'Elanna Torres is the only one among the crew to realise that they must have traveled through a Portal Network.
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Atomic Rockets has black hole reactors as an exotic powerplant type. By using a relatively small black hole (with mass "insignificant" next to the 10^14th KG-about one million billion kilograms-weight of the engine) spherical graphene absorber to soak up the singularity's radiation and re-radiate it as heat for a blackbody-radiation engine, the whole mess should be powerful enough to fly a ship the size of a good-sized space station, even if it was all habitation module, and wouldn't need to be refueled for several million years. The big problem is actually making a black hole (and getting, quite literally, a jillion tons of graphene), as most concepts involve near-lightspeed acceleration (in which case, you already have a viable engine so why bother?) or Gamma-Ray lasers (which we can't make until we find something that can focus/reflect Gamma-Rays). It would be more easy to find natural black holes and make them suitable for our uses. A later (that is, lower down on the same page) article deals with methods of electrically charging (so it can be held in place with magnets) and spinning up a singularity for use.
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 Atomic Rockets (Website)
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Space Station 13: The Goonstation and /tg/station servers feature a Singularity Engine as a powerful but dangerous power source. Should the singularity get loose, it will wander around the station destroying everything it touches. Stopping it requires either careful use of explosives (Goonstation) or sacrifices (/tg/station), and even they aren't foolproof. To emphasize the danger, the Goonstation wiki's heading on rogue singularities is labeled "Uh Oh", and /tg/station has dubbed the singularity "Lord Singuloth".
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In Sid Meier's Alpha Centauri any faction, once it is advanced enough, is capable of equipping its bases and units with singularity drives. Of particular note, the destructive yield of any Planet Buster equipped with such a power source is downright terrifying.
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 Sid Meier's Alpha Centauri (Video Game)
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The Outer Limits (1995): In "Trial By Fire", aliens drop a safely contained black hole on the moon. Scientists suspect it is a gift to provide humanity a potentially limitless source of energy.
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 The Outer Limits (1995)
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Marvel Two-in-One Annual #5 had Pluto attempt to use a device to overload a black hole in the hopes of destroying the universe so he could rule over eternal darkness. The Hulk and the Thing foiled this centuries-long plan by smashing the ground underneath him really hard so he fell into his machine.
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 Marvel Two-in-One (Comic Book)
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Alice Grove: The title character and other pre-apocalyptic Super Soldiers are quantum entangled with black holes to fuel their strength, speed, and toughess.
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 Alice Grove (Webcomic)
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SCP Foundation: Prometheus Labs proposes building a spacecraft like this, using a microscopic black hole's Hawking radiation to accelerate and power the ship.
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 SCP Foundation (Website)
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The Ganymeans in The Giants Series use spinning artificial singularities to power their ships. The Thuriens take it to a higher level, using the spinning singularities to create portals through space and time; large portals to carry people and ships, or tiny portals to carry information and power. They generate the immense amounts of power that their civilization needs with stellar-scale artificial black holes.
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 Giants Series
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A Certain Scientific Railgun: A biological example. Kimi Shundan has the power to create black holes and later becomes able to summon a dragon. It is discovered that the dragon is feeding on the black hole to become stronger. Some scientists speculate that if she can get better control of her power, they would be able to harness the black hole as an energy source.
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 A Certain Scientific Railgun (Manga)
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In Schlock Mercenary the supermassive black hole at the center of the Milky way is turned into a toroidal shape via a special project and acts as a giant zero-point energy source. It was almost sabotaged to be a bomb that rewrites reality.
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Isaac Arthur has done multiple videos about using black holes as power generators. Including: Colonizing Black Holes, Black Hole Ships, and Weaponizing Black Holes.
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 Isaac Arthur (Web Video)
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EVE Online: starships designed by the Triglavian faction utilize naked singularities contained on the external hull as their vessel's primary power source.
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Brainiac's ship is powered by six miniature black holes in Superman: Red Son. He primes them to go off when he's defeated so Superman has to make a Heroic Sacrifice and fly the ship away from Earth.
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 Superman: Red Son (Comic Book)
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Super Robot Wars provides two very different examples among its series-original units.
The Huckebeins are a series of Gundam Expy mechs which serve as high-performance Real Robots, using gravity-based Energy Weapons and Deflector Shields powered by a Black Hole Engine.
In the Classic continuity the Huckebein is a one-of-a-kind unit designed for the exclusive use of the protagonist, being the Real Robot counterpart to the Super Robot Grungust.
In the Alpha continuity the Huckebein is one of the first units constructed from Extra-Over Technology (a hoard of alien Black Box tech recovered from a meteor), and its Black Hole Engine was abandoned in favour of more conventional reactors after one of the test units went haywire in the infamous "Vanishing Trooper" incident. It's later revealed that the Balmarian Empire let humanity find a deliberately-flawed engine as a Secret Test of whether they were advanced enough to become a threat - one which was sabotaged by Ingram Plissken and Shu Shirakawa in order to buy Earth more time.
The Original Generation Huckebein's history is similar to its Alpha counterpart, except that its Black Hole Engine was retrofitted onto a design already in development, and the flaw in the engine was introduced by the Zuvorg Alliance (a rival group of aliens) either supplying that technology themselves or tampering with it for their own purposes.
The Granzon was originally created as an unlimited-budget testbed for EOT, including the Huckebein's Black Hole Engine. Its designer and pilot Shu Shirakawa somehow managed to upgrade it into the unique Annihilation Engine, which incorporates three contained singularities and a matter-antimatter reaction to achieve performance and stability actually higher than what even the Zuvorg are capable of. And then he enhanced it with magic from La Gias just for good measure. Put together, the Granzon jumps straight past "Super Robot" into "God-like Robot" territory, capable of creating weaponized black holes, wormholes, and a gravitational warp field that protects it from attacks.
The Granzon is later upgraded into the Neo Granzon, enhancing all its abilities and unlocking an even more powerful attack in the form of the Particle Degeneration Cannon (a Sphere of Destruction resembling a white hole).
In the Original Generation continuity it's revealed that due to Shu improving the Engine without fixing its original flaw, he has been unknowingly thinning the boundaries between realities - turning the Granzon into a Weirdness Magnet which has been drawing aliens and extradimensional beings to Earth.
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Overwatch alludes to this with the character Sigma, who received gravity-based superpowers after a Freak Lab Accident exposed him to the raw force of a miniature black hole. Among his in-game abilities is "Accretion", a defensive ability where he creates a small black hole in the palm of his hand that not only absorbs and nullifies enemy fire, but converts it into "shields" to keep him sturdy.
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Stargate SG-1: Stargates can be powered by black holes.
This first discovered by accident in "A Matter of Time" when an attempt to retrieve a missing SG team Goes Horribly Wrong: the SGC unwittingly dials a gate on a planet whose sun has just become a black hole, and the gate becomes stuck to that destination, remaining open even after the power from the SGC side is disconnected.
In "Beachhead", the Ori use a force field projected through a stargate to forcibly collapse the planet in question below its Schwarzchild radius, creating a micro-black hole that is used to power a "super-gate" big enough to send the Oris' invasion fleet through from their home galaxy. That attempt is foiled. Their next, in the season finale, is not.
In "The Pegasus Project", the SGC successfully blockades the super-gate by placing one normal stargate next to it, and another next to a solar mass black hole, then detonating a nuclear warhead through the wormhole to energize the super-gate and force it to connect to the black hole, rendering it useless to the Ori.
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The Quantum Thief: In The Causal Angel, the Phantom Thief Jean le Flambeur's ship Leblanc has a black hole that emits Hawking radiation which is used for propulsion. The zoku Gun Club also uses contained black holes, only in their case they focus the emitted Hawking radiation into a devastating Wave-Motion Gun.
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The Original Generation Huckebein's history is similar to its Alpha counterpart, except that its Black Hole Engine was retrofitted onto a design already in development, and the flaw in the engine was introduced by the Zuvorg Alliance (a rival group of aliens) either supplying that technology themselves or tampering with it for their own purposes.
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 Super Robot Wars: Original Generation (Video Game)
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Star Trek
The Star Trek: The Next Generation Writers' Technical Manual states that the Romulan D'Deridex-class warbird is believed to be powered by x-ray emissions from a captured microsingularity, rather than fusion and matter/antimatter reactors like most other ships. Star Trek canon has usually adhered to this since then, Depending on the Writer, and it is sometimes used as a plot point:
TNG episode "Timescape", when an alien species' attempts to incubate their offspring in the artificial singularity core of a Romulan warbird (as opposed to the natural singularities they would normally use) results in fracturing local space-time when the Enterprise-D comes to assist the warbird after a Distress Call.
Exploited in the Star Trek: Deep Space Nine episode "Visionary" when the crew are able to locate a cloaked warbird by hunting for the emissions of its drive singularity.
In Season 4 of Star Trek: Voyager, the crew come across a Lost Technology relay network that spans a large part of the galaxy, enabling them to finally communicate with Starfleet. Unfortunately to destroy a Hirogen hunting party Captain Janeway destabilizes the micro-black hole powering a relay station, accidentally crashing the entire network.
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In The Loud House episode "The Mad Scientist", Lisa invents a Time Machine that involves both a black hole and a wormhole in its construction.
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Xenonauts: While the first alien ships are powered by alenium batteries, the biggest ones, the ones capable of charging those alenium batteries, draw power from a "singularity core" which is explicitly said to be based on a black hole.
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The Transformers: Unicron: In the same continuity as Transformers: Devastation, the Planet Eater Unicron draws power from a black hole at its core, but indirectly; it actually exploits the black hole's quantum tunneling effects to drain energy from nearby stars, causing them to dwindle and vanish every time it successfully eats a world.
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In the Alpha continuity the Huckebein is one of the first units constructed from Extra-Over Technology (a hoard of alien Black Box tech recovered from a meteor), and its Black Hole Engine was abandoned in favour of more conventional reactors after one of the test units went haywire in the infamous "Vanishing Trooper" incident. It's later revealed that the Balmarian Empire let humanity find a deliberately-flawed engine as a Secret Test of whether they were advanced enough to become a threat - one which was sabotaged by Ingram Plissken and Shu Shirakawa in order to buy Earth more time.
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 Super Robot Wars Alpha (Video Game)
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Foundation (2021): Imperial ships have a large negative space in their hulls, which generate a black hole to power their Alcubierre Drives.
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The prospect of generating energy with black holes is brought up several times in Aeon 14.
Discussed in Destiny Lost. Shenanigans involving an Earth-Shattering Kaboom result in a brown dwarf in the Bollam's World System being compressed into a black hole by a massive fusion explosion. The brown dwarf had been artificially inflated with gravity fields to generate helium-3 for fusion fuel, but the protagonists remark that the Bollers could actually get more energy by harnessing the new black hole as a power source.
DMGs emerge during the Orion War as a Wave-Motion Gun capable of overwhelming the ISF's formerly invulnerable stasis shields. The problem is, they require so much energy that they have to be fixed into a hollowed-out moon so that they can be powered by a captured singularity. The second time a DMG emplacement is encountered, damage from the Transcend Space Force's counterattack causes it to break loose, eat the moon, and enter a decaying orbit around the planet. The Intrepid Space Force adapts the DMG to run on vacuum energy instead, enabling them to be mounted on their own I-class motherships.
In Race Across Spacetime, the Core AIs are shown dumping stars into Sagittarius A*, the supermassive black hole at the core of the Milky Way, to power massive computers for complex calculations.
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Doctor Who: Rassilon was able to harness the power of a Black Hole in an "Eye of Harmony", which sits under the Panopticon in the center of the Time Lord Citadel.
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Outer Wilds: The Nomai manufactured black holes and corresponding white holes for teleportation, on a small level using one-way warp pads to transport people between locations, and in the large scale putting both together in a “warp core� that allowed their ships to jump vast distances in space instantly. However, their most important known utility comes from exploiting their weird temporal properties to send information backwards in time. The Nomai, searching for a mysterious object beyond the solar system with an unknown location, used a warp core to create a time loop in which they’d fire a probe into deep space on a randomized trajectory, and the iteration that found it would retroactively transmit the coordinates back to base, so that the Nomai would have its location on the “first try�.
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The Persistence's engines runs off the gravitational energy created by a singularity. The same energy is used in a much smaller form to power your Gravity Grenades.
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Portal: Aperture Investment Opportunity #4: "Boots" implies this for the Portal Gun, because it can stop working if the Miniature Black Hole inside fails.
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Star Carrier: For power needs too great for fusion reactors, such as spaceships, humans make use of quantum power taps, consisting of two microsingularities shielded by Higgs fields orbiting each other at relativistic speeds, which essentially allows them to pull energy from vacuum.
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Stellaris:
In the base game, black holes can produce dark matter, which can be used, among others, in some ship reactors to power them.
The Megastructures DLC uses them not for energy but for mining, with the Matter Decompressor that extracts from the mass the black hole has accumulated for millennia.
The Gigastructural Engineering mod adds a few more options. If you just need a power generator, you can build a Penrose Sphere around a black hole and let the constant reflection between the latter and the sphere's mirrored insides generate energy. If you're thinking big, you can work on this principle until you get a Birch World, an unfathomably huge Habitat that uses the black hole for both gravity and power, and has essentially unlimited space for habitation.
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Star Wars Legends: According to one of the guidebooks for Attack of the Clones, gravitational devices such as repulsorlifts, tractor beams, and accelerator compensators were built in unmanned energy refineries that were constructed around black holes to harvest the energy emitted from them.
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Quake II has the level "Launch Command", from the Hangar Unit, where the objective is to destroy a computer controlling the Black Hole Generator, seen at the beginning of the level, which provides energy to Strogg mechanisms that allow the race to travel to other universes.
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In Dyson Sphere Program, Dyson Spheres (which were originally conceived as solar energy collectors) can be built around black holes.
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In Event Horizon, the eponymous starship uses an artificial black hole drive to achieve faster-than-light travel. Being that it's a supernatural horror movie as well, Hyperspace Is a Scary Place.
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In Season 4 of Star Trek: Voyager, the crew come across a Lost Technology relay network that spans a large part of the galaxy, enabling them to finally communicate with Starfleet. Unfortunately to destroy a Hirogen hunting party Captain Janeway destabilizes the micro-black hole powering a relay station, accidentally crashing the entire network.
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Transformers:
Transformers: Devastation: Sixshot boasts that he's powered by a hermetically sealed singularity when Optimus Prime first confronts him. Rather than intimidating Prime into surrendering, it instead motivates him to order the Autobots to disengage the power inhibitors on their weapons because they can't afford to worry about collateral damage when faced with such a powerful foe.
The Transformers: Unicron: In the same continuity as Transformers: Devastation, the Planet Eater Unicron draws power from a black hole at its core, but indirectly; it actually exploits the black hole's quantum tunneling effects to drain energy from nearby stars, causing them to dwindle and vanish every time it successfully eats a world.
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The World at the End of Time: Near the end of the book, in a very distant future when all stars have burned out and the only energy source available is proton decay, Wan-To is seriously considering to move to a black hole and live off the extremely feeble Hawking radiation, knowing protons will sooner or later be no more.
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The Star Trek: The Next Generation Writers' Technical Manual states that the Romulan D'Deridex-class warbird is believed to be powered by x-ray emissions from a captured microsingularity, rather than fusion and matter/antimatter reactors like most other ships. Star Trek canon has usually adhered to this since then, Depending on the Writer, and it is sometimes used as a plot point:
TNG episode "Timescape", when an alien species' attempts to incubate their offspring in the artificial singularity core of a Romulan warbird (as opposed to the natural singularities they would normally use) results in fracturing local space-time when the Enterprise-D comes to assist the warbird after a Distress Call.
Exploited in the Star Trek: Deep Space Nine episode "Visionary" when the crew are able to locate a cloaked warbird by hunting for the emissions of its drive singularity.
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Futuristic Tech Index
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Gravity Tropes
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