# Is a particle beam the best method to fire a black hole at a target?

I want to weaponize black holes as projectile attacks in my story from small to supermassive and the two ways i can think of is using mass to attract mass or using matter to push it. Using a particle beam to push a black hole seems like the better options as it will not only push it but it will feed it, this will help with smaller black holes that would evaporate on the journey to the target.

I assume the feeding black hole will have an accretion disk and possibly a quasar depending on its size. For the super and ultra massive black holes Nicoll-Dyson beams or multiple to thousands or more stars could fire particle beams to move it to a destination or target.

My question is, is a particle beam actually capable of moving small (larger than atoms so they can feed and be pushed) and supermassive black holes to high velocities or is there are better method?

• Any black hole is created of atoms, so it should be bigger ;). Unless there's electron black holes or something which I don't know about. Aug 7, 2020 at 14:34
• @Trioxidane I wanted to evade answers of sub atomic black holes, the BH needs to be able to be pushed and possibly fed so larger than sub atomic scales.
– user78658
Aug 7, 2020 at 15:01

I would be quite surprised if a Nicoll-Dyson beam is capable of moving a stellar-mass or supermassive black hole without taking many centuries (or millions of years) to do so.

Let's say our black hole has a mass 10 million times that of the Sun, and let's say we want it to reach a velocity of $$\sim100\;\text{km/s}$$ relative to its current rest frame, which I'd say is a reasonable velocity by the standards of astronomical objects. If our beam was to capture and reuse all of the output power of the Sun, it would need to collect solar energy for a time $$\tau=\frac{\frac{1}{2}Mv^2}{P}=\frac{\frac{1}{2}10^7M_{\odot}(100\;\text{km/s})^2}{L_{\odot}}\approx10^{13}\;\text{years}$$ If we choose a more luminous star, we might be able to reduce that by maybe 4-5 orders of magnitude, but it still involves gathering energy for 100 million to 1 billion years. If we choose an ensemble of stars, maybe we can force that down by a couple of orders of magnitude, but it's still rather high.

This becomes drastically more manageable in the case of a stellar-mass black hole, which might weigh in at a few tens of solar masses. Now we're looking at gathering energy from a luminous star for only a few centuries. However, we have a new problem: It's quite hard to focus all of that energy onto a stellar-mass black hole. A black hole of $$M=10M_{\odot}$$ is about 60 km in diameter. Taking into account the fact that its gravity will drastically bend spacetime, I'd argue that its true cross-section is a bit larger, but not by much.

This means that only a fraction of our beam will actually transfer its energy to the black hole, and it will in turn take much more time than expected to help it reach the desired speed. Even if our beam is highly collimated, it will still spread out enough over interstellar distances. I think we can now increase our wait time by at least an order of magnitude, likely more.

For lighter black holes, this may work. I believe a black hole of $$\sim10^9$$ kg will take less than a day to evaporate, so we can call that "stable" (and as the evaporation time scales as $$t\propto M^3$$, let's assume that our tiny black hole is no less massive than that by a factor of a few). Now, if we were to focus all the light of the Sun on that black hole, we could reach the desired speed in about a nanosecond. Indeed, to get it to more human-sized speeds, we could perhaps even do without a source anywhere near as luminous as the Sun.

It's tempting to explore other options which wouldn't work for the larger, more massive astrophysical black holes, like particle accelerators. If the black hole was charged, we could use magnetic fields to accelerate it to high speeds. Unfortunately, this would require a substantial amount of energy. Our black hole is $$10^{34}$$ times as massive as a proton, and our particle accelerators are presumably incapable of accelerating an object that massive to any significant speed.

As a concrete example, a cyclotron must output an energy of $$E=\frac{q^2B^2R^2}{2M}$$ to move a particle of charge $$q$$ and mass $$M$$ in a circle of radius $$R$$ in a magnetic field $$B$$. We see that we then have to make up 34 orders of magnitude in the numerator. Even if the black hole was significantly charged, we would need an enormous accelerator with strong magnetic fields, which I find unlikely.

Now, you want our black holes to be larger than atoms. If you're talking about that in terms of mass, well, we're already at the lower limit of black holes which can remain stable for significant periods of time. If you're talking about that in terms of radius, we'd need a black hole with a Schwarzschild radius of about an ångström, or $$10^{-10}$$ meters. This requires a black hole of mass greater than $$M>6.7\times10^{16}\;\text{kg}$$, which poses even more problems than before. I think this definitively rules out particle accelerators, and all reasonable methods using present-day technology for moving tiny things very quickly.

• Although it's not technically part of the question - if you did accelerate a black hole in this fashion, how would you steer? Aug 7, 2020 at 15:40
• @Cadence Very carefully? More seriously, a small black hole could be steered by magnetic fields, if it's charged, while a stellar-mass or supermassive black hole might be harder to steer - additional beams would be needed. Aug 7, 2020 at 15:42
• @HDE226868 I had forgotten about the particle accelerator method for smaller bh's, would the energy from the magnetic fields feed the bh also so that it doesnt evaporate or would a beam need to be added for that?
– user78658
Aug 8, 2020 at 10:08

Assuming physics still apply the general formula for force is:
F(orce) = m(ass) * a(cceleration)
rewriting this, we get:
a = F / m
if you want to accelerate the black hole you need to consider the mass of the black hole. The masses do vary, but in general normal black holes are pretty heavy.
You need to apply A **** LOT OF FORCE

Your idea was to use other mass to interact with a black hole (with kinetic impulse transfer) to accelerate the black hole. So lets do some math:
Wikipedia says a normal black hole has 5 - 10 solar masses, which are about 2 * 10^30 kg, so lets go with 1.5 * 10^31. If you want to "push" the black hole to 1m/s
(that actually a pretty low speed for a projectile, but if you shoot it at an immobile target it should be enough)

Lets choose a projectile to shoot our "projectile" (black hole):
We could shoot an arrow, a bullet, or an atom.
I want high numbers, so i'll go for the electron :D.
an electron 'weights' about 9.10938356 * 10^-31 ; for simplicity 1 * 10^-30

The formula is:
v(elocity) * m(ass) = i(mpulse)
i = i v * m = v * m black hole speed * black hole mass = speed of shot electron * mass of electron 1 (m/s) * 1.5 * 10^31 (kg) = x (m/s) * 1 * 10^-30 (kg)
1.5 * 10^31 = x * 10^-30
1.5 * 10^31 / 10^-30 = x
1.5 * 10^61 = x (m/s)

For comparison:
lightspeed is 299 792 458 m/s or 3 * 10^8.
were closely outspeeding every traffic speed limit there is.

For comparison: the known universe is about 9,3016 × 10^10 light years in size lets go with 110^11;
1
10^11 * 31556952 seconds per year * 3*10^8 m/s ~ 946.708.560.000.000.000.000.000.000
~ 10^27 m
our electron with 1.5 * 10^61 m/s would traverse the known universe in less than a second

Lets go with an arrow of the weight of 0.1 kg.
That would still reach an amazing speed of 1.5 * 10^30 and would travel the known Universe in less than a second.
At this point you may just shoot it at your enemy directly because that may be even more lethal than a black hole.
How that would look like

Hope it helps

• I want to note that this uses Newtonian mechanics, which doesn't work when dealing with relativistic speeds. If you use the relativistic equations, you'll find that the object may travel very close to the speed of light, but won't pass it. On another note, welcome to Worldbuilding Stack Exchange! I hope you stick around. Aug 7, 2020 at 15:52
• im here longer, i just dont have/want an account :D and youre probably right with relativistic speed i just want to exagerate and play with the numbers :D Aug 7, 2020 at 16:28