Moving a black hole

Question

What (if any) would be a viable option for moving a black hole with a similar mass to our moon? The black hole is not very far away (i.e disregard difficulties in reaching it). Ideally, there should be a deployable option for both short and long distances (at least 0.5 light years)(short and long distances can have separate methods). Obviously, mounting physical thrusters is impossible, so is there a different way of "pushing" one?

Answer 1

Black holes are not particularly special when considered far from the event horizon. They behave like any object with mass, charge, angular momentum, they follow geodesics, and so on. When fields are weak and speeds are low, GR behaves like Newtonian mechanics.

Momentum transfer

So, right off the bat, one way you can move a black hole is to crash a projectile into it, something with a lot of momentum to donate.

$$p=m_{p}v$$

As mass of the projectile, $m_p$, decreases, its velocity must increase to maintain the same momentum. If the black hole fully absorbs the projectile and nothing is scattered, then it gains all of the projectile's momentum. You can calculate the delta-v inflicted on the black hole by rearranging the momentum equation:

$$Δv=\frac{p}{M}$$

Where $M$ is the mass of the black hole, $7.35\cdot10^{22}$ kg. First, let's find the size of the black hole to figure the size of the projectiles, in order to fully intersect with the black hole's cross-sectional area. The radius of a Schwarzschild black hole is given by:

$$r=\frac{2GM}{c^{2}}$$

This comes out to 0.2 mm in diameter. Let's make the projectiles 0.1 mm across, just to be safe, and assume they're made of iron with density 7,900 kg/m^3. Projectile mass comes out to $3.3\cdot10^{-8}$ kg. Vanishingly small. Maybe ultra-high speeds will make up for the lack of mass?
If the iron spheres move at fully half-lightspeed, they each impart $6.8\cdot10^{-23}$ m/s delta-v. Yikes.
Presumably you've got a linear accelerator shooting these things like mad, and macron accelerators can be quite efficient at translating electrical energy to kinetic energy, but even after a combined one billion projectiles the total delta-v inflicted on the black hole is $6.8\cdot10^{-14}$ m/s. Maybe you've got one long'n accelerator, so let's look at higher speeds. To do that we'll need to use the formula for relativistic momentum instead:

$$p_{R}=\frac{m_{p}v}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$$

One of these projectiles moving at $0.999999997$ c imparts a delta-v of $1.65\cdot10^{-18}$ m/s, and one billion yields a combined $1.65\cdot10^{-9}$ m/s. Yikes, still.

Now, a macron accelerator scaled for the job at hand could probably churn out millions of these particles, and over time it would have an effect. An accelerator shooting one million every second for a year will have imparted 0.00005 m/s delta-v, displaced the black hole by 0.0008 m, and raised the black hole mass by 1,000,000 kg. It would take 35 years and 36,000 metric tonnes of iron macrons to move the black hole 1 meter.

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Electrostatic accelerator

A better option might be to give the black hole an incredible charge and stick it in an electrostatic accelerator. Charged objects feel a force when placed between electrodes, proportional to the accelerator voltage gradient and the object's charge. The exit velocity of a particle through a linear electrostatic accelerator is given by:

$$v_{exit}=\sqrt{2V\frac{C}{M}}$$

$V$ is the difference in voltage, $C$ is the surface charge on the object, and $M$ is the mass of the object. The surface charge can be found by:

$$C=4\pi ε_{0}V_{g}r^{2}$$

$V_g$ is the voltage gradient across the object and $r$ is the object's radius. With a voltage gradient of 100M V/m and black hole radius of 0.0001 m I get a surface charge of $1.11\cdot10^{-10}$ Coulombs. Going back to the first equation, if the voltage gradient across the accelerator is 100M volts, I get an exit velocity of $5.5\cdot10^{-13}$ m/s.
(Disclaimer, I'm not sure whether some of these voltage figures are "reasonable", even for extrapolated super sci-fi tech.)

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Black hole rocket

Linear accelerator is out, and it seems there's no easy way to do this.

Here's my suggestion: you've got a black hole that's just the right size for power generation via matter accretion (you could get away with smaller, but a tenth of a millimeter is probably okay). If memory serves, micro black holes have the potential for 40% mass-energy conversion, which is on par, if not better, than matter-antimatter efficiencies. If you dump a lot of charged matter into the black hole, you can pin it in a powerful magnetic field and draw power from the emitted radiation of accretion, and probably the magnetic pressure of containment as well. You're probably looking at petawatts of power, minimum, which could be used to power an efficient electric thruster.

Alternatively, you might use the accretion energy to heat reaction mass like hydrogen to extreme temperatures and thrust off of it with a magnetic nozzle, creating a very efficient thermal rocket; or, you might redirect some of the super-hot accretion matter itself as exhaust.

Ballparking some figures, if your black hole rocket has 1 Lunar mass of hydrogen fuel (mass ratio of 2) and can expel the hydrogen at an exhaust velocity of 30% c, then delta-v comes out to ~7% c, enough for a boost up to 3.5% c and back down again. With a mass flow of (ballparking here) 10,000,000 kg/s (VERY high), we get a thrust of $3\cdot10^{14}$ N, an acceleration of $4.1\cdot10^{-9}$ m/s^2, and a burn time (the time it takes to burn all reaction mass) of 230 million years. To get burn time into timescales measured in centuries, mass flow needs to increase to 10 trillion kg/s, which is just downright unrealistic (that's like 1 Mount Everest every second).

Clearly, the black hole doing all its own pushing isn't going to cut it. (There probably exists an equilibrium though where a small enough black hole (that's not too small for accretion) can manage mass flows that equate to burn times on human timescales.) Clearly, the black hole needs outside help. I would suggest using some of the black hole's accretion energy for thrust, diverting the rest to magnetic confinement, and using external propulsion such as beamed power from a large solar array. A large laser sail, or magnetic sail, tethered to the black hole containment machinery, receiving exawatts of equivalent thrust power to seriously boost it up to speed. The sails would have to be quite large, probably thousands of kilometers across, to achieve enough collection area for beam power.

Once you've got it up to speed, you'd definitely make use of gravitational assists and slingshot maneuvers where and when you can.

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At the end of the day, you're trying to move something as heavy as the Moon, and that's going to be costly no matter which way you look at it.

Answer 2

TL;DR: the energy requirements for moving a black hole over even slightly interstellar distances (eg. your 0.5ly journey) are so unreasonable as to be out of the reach of anything but a Kardashev level 2 civilization, and therefore practically godlike by our standards. No merely human-level things are plausibly going to be able to do what you ask.

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The Dying Of The Light mentioned gravity tractors, and that's one way in which you might move a massive object without physically attaching rockets to it or waving your hands and invoking sufficiently advanced technology. This basically involves another massive object "hovering" near the thing you're trying to move, using its own reaction motors to stop it falling into the payload, and relying on the mutual gravitational attraction of the payload and tug to drag the payload.

The mass of the tug is given by $$m_2 = \frac{Fr^2}{Gm_1}$$ where $F$ is the desired force to impart to the payload, $r$ is the separation of the tug and the payload, $m_2$ is the mass of the payload (eg. the mass of the moon in this case) and $G$ is the gravitational constant. In the simplest-to-calculate case, lets do a continuous thrust uniform acceleration brachistochrone transit to move the black hole 0.5ly in 1000 years. This requires an acceleration of approximately 2 microgees, giving a thrust of about 1.4 exanewtons (1.4x10¹⁸N). If you positioned your tug a mere 100km away from the black hole (black hole gravitational field strength of 50 gees) then its mass could be as low as 2.8x10¹⁵kg. If it were 1000km away, the mass requirement increases to 2.8x10¹⁷kg, but that's still 5 orders of magnitude smaller than the moon. For comparison, Saturn's moon Calypso has appoximately the mass of the former, andhas a mean radius of ~10km. Elara, a moon of Jupiter, has the mass of the larger tug and has a mean radius of ~80km.

The transit has a total delta-V of ~600km/s. A beam-core rocket with an exhaust velocity of 0.3c would necessitate a mass ratio of only 1.007, which is pretty reasonable giving a ballpark antimatter requirement of about 2.5x10²⁰kg (plus the same amount againt of the regular stuff)... for reference, Enceladus is about 10²⁰kg, so your total propellant supply is equivalent to about five enceladuses. You'd probably park them in higher orbits around the black hole such that they wouldn't ever block the thrust plume of the big rocket.

(side-note: you can't easily use the black hole itself for power generation here, because its Bekenstein-Hawking luminosity is a fraction of a watt... you might be able to build an accretion disk and use that as a power source, but that adds a non-trivial amount of mass and has its own problems which are too complex for me to examine here, mostly around how big the hot region of an accretion disk around a lunar-mass black hole could actually be)

Producing that much antimatter, and transporting half a lightyear, and then maintaining it for a millenium and tapping it safely and burning it efficiently throughout that time is left as an exercise to the reader, who probably needs to be about level 2 on the Kardashev scale... if you had a Dyson sphere that could perfectly capture the output of the Sun, it'd take you its full output for a few thousand years to synthesize enough antimatter ex nihilo, and at that point you gotta wonder if it would be easier to just build a Kugelblitz generator instead.

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So much for rockets. Now we've established you need the capability to be building and using (possibly partial) Dyson swarms, why not avoid all that tedious and ganderous mucking about with moon-sized chunks of antimatter and instead use a light sail as your gravity tug and point a Nicoll-Dyson beam at it. If you're not pushing the black hole directly away from your source emitter, and directly towards a braking emitter of similar power this becomes harder, but I'll handwave those difficulties away because you're basically dealing with ancient and strongly superhuman star-gods at this point.

Lightsails accelerate because photons have momentum. From The Starflight Handbook, if a beam of light with power $E_b$ is perfectly reflected by a sail of mass $M_s$, then that sail will experience a change in velocity $\dot{V_s} = {2E_b \over M_s c}$.

To achieve your microgee-level acceleration with a moon-like mass pulled by a solar sail (on the assumption that the sail mass is much less than the total mass of sail-plus-moon system) you need about 2x10²⁶ W... that's about 1.8 times the luminosity of the Sun, so you need either multiple small beam sources or a brighter star (of at least F8V type). And remember, you need a similar star at the other end to brake the 'hole into place at its destination!

If the sail was irradiated with 1MW/m² of laser energy, it would need to be a disc some 8 million kilometres in radius (about 0.05AU), and if it was made of something that weighed 1g per m², it'd mass about 2.1x10¹⁷kg. Keeping it attached and in shape is left as an exercise to the reader, but as the users would be K2-level civilisations, they shouldn't find this to be particularly challenging.

Flight time would be 1000 years, as with the antimatter rocket above. There'd be no fuel synthesis time, though that's offset by the need to build multiple ND-beams. Again, it isn't clear how useful a little black hole would be if you could wield this sort of power, but that's a plot-level discussion out of scope of this answer.

Answer 3

Alright, lets see.

A Black Hole with the mass of the Moon, assuming it doesn't rotate, has a Event Horizon 0.2mm across. So 0.10644mm in Radius. This would make it exceptionally dangerous and hard to spot.

This small size rules out basically everything the two others have said because of two facts of life.

1. Such a small Black Hole has an insane gravitational acceleration on its Surface (The Event Horizon) so putting ANYTHING even remotely close to it won't fly as the Tidal forces will shred anything into a string of atoms. To be exact, the Acceleration due to gravity at the Horizon is 422197661110932750455m/s². At a distance of 1000km the acceleration due to gravity would be about 4.22m/s². Give or take. 100km out, the acceleration is 422m/s² and so on. So dropping anything in is not a good idea. The main reason is that everything will get shredded. So your debris wont enter all on the same side. Quiet the opposite. Due to the strong acceleration the debris will kinda fall in from all sides. If they don't get yeeted into interstellar space.
2. The black hole is so small that whatever you throw towards it is more likely to just get shredded into a billion pieces and be thrown away instead of falling in. It is actually rather hard to let something fall into a black hole this small.
3. The Black Hole has way too much inertia anyways. Shooting at it is the equivalent of firing a 9mm at the moon and expecting it to move.

These reasons also apply to very large Black holes. The Gravitational field and Inertia make it basically impossible to move them.

There is one way to do it though. With Lasers. If you fire a Laser with a wavelength at least half as big as the Radius of the Black Hole, you can transfer the Momentum of the Photons to it with basically 100% efficiency. The higher wavelength the laser is, the more Energy and hence momentum you transfer.

Yet still, here is where it all kind of falls apart. A Black Hole the size of the Moon is just a mass the size of the Moon trying to be moved with a laser pointer. We can do the math here but the verdict is that if you don't have the power of a Star focused into a beam 0.005mm in radius you ain't gonna move it.

Answer 4

Feed it with a moving mass

Everything Glorfindel said holds. You won't be able to approach this object.

Its size is only 2mm or moon weight, it could be 2 moon weights, still no immediate danger to the planet. Now consider feeding it a moon, or a large asteroid, in order to move it.

All you have to do is disturb e.g. Phobos orbit around Mars in such a way, that it will collide the tiny black hole at some velocity. After the collision, Phobos will be eaten by the black hole, or it flies through, but some of the momentum Phobos had will be added to the momentum of the black hole, pushing it out of orbit. Note: calculation is required, there should be relevant friction !