# Would the gravitational waves from a binary black hole system make a feasible weapon?

Backstory: Okay, so we have decided to wage war on numahs for the macguffenite. We mostly are doing things like shooting lasers at each other ships, and occasionally shooting high velocity projectiles at each other. The humans than come up with a plan. The plan is to hit the numah bases with a bunch of micro black hole missiles (which have an explosive amount of hawking radiation at the end of their life) and then throw a couple planetary mass black holes to eat up their bases and suns and what not. Have way through gathering up all the resources, one of our space diplomats/explorer discovers that in space, they have a set of treaties governing space warfare (which applies whether you signed it or not.) One of the rules (which I shall conveniently translated to English for you is

No space civilization shall cause a black hole to enter a system of another civilization for the purposes of gravitationally disrupting or accreting the persons or properties of that civilization, nor shall they expose the persons or properties of any civilization to damaging levels of black hole particle emissions (hawking radiation).

So well, darn, are we were all ready to start making our black holes. It also turns out that the last civilization to violate the treaty got pelted by antimatter rail guns, so that is out of the question. What are going to do with our black holes now. Wait, is there a loophole?

Question: How feasible of a weapon would it be to set two rather massive black holes in rapid orbit around each other, for the purpose of generating gravitational waves?

• How large would the black holes have to be, and how fast would they have to spin?
• How would you prevent them from ramming into each other?
• What would be the effective range of the weapon?
• How do we not hit ourselves?
• Will it violate the space warfare treaty (the answer is yes, but the humans don't know that yet (the humans should study more carefully))
• I'm assuming that energy loss from a binary black hole system would be a decent gauge of its ability to function as a weapon. – Green Aug 3 '15 at 22:12
• See the chapter 4.2 of this article but it is dealing with 2 neutron stars instead. I'm intimidated by the mathematics, imagine what if... – user6760 Aug 4 '15 at 2:49

## No, this would not be a feasible weapon.

Although I originally posted an answer to this question five years ago, I've since deleted it and am starting anew. One reason I deleted it is that the answer only tangentially addressed the question, despite receiving some upvotes. The other reason is that the portion that does, in my opinion, adequately work towards a proper answer takes the wrong approach. I tried to assess the feasibility of such a weapon by discussing the power radiated by two merging stellar-mass black holes; instead, I should have chosen a quantity that is distinctly characteristic of gravitational waves: strain.

The strain, $$h$$, of a gravitational wave is a measure of how much spacetime is distorted by the passing wave. If you have an object of length $$L$$, it will be alternatingly stretched and compressed by a distance $$\Delta L=hL$$. This is the principle behind the interferometric techniques used by LIGO to observe gravitational waves in the first place.

Say you're a distance $$r$$ from a pair of binary black holes of total mass $$M$$. During any point in their coalescence, you can assign them an effective velocity, $$v/c$$, which increases as the black holes move closer and closer together. The peak strain you measure is then roughly $$h\sim\frac{GM}{c^2}\frac{1}{r}\left(\frac{v}{c}\right)^2$$ Consider the case of the first detection of gravitational waves. That merger involved two black holes of about $$30M_{\odot}$$ apiece (and therefore a total mass $$M\approx60M_{\odot}$$), lying a distance $$r=410\text{ Mpc}$$ away. Shortly before coalescence, their effective velocity was $$v/c\approx0.6$$. Plug in the numbers and you find that the strain at that moment, as measured on Earth, should be $$h\sim10^{-21}$$, which is what was observed by LIGO. That's tiny! Now let's say we're standing a few light-years away from the source - say, $$r=1.34\text{ pc}$$, the distance from Earth to Alpha Centauri. Now we reach a much larger strain, $$h\sim10^{-14}$$ - still a pittance. Even at a distance of 1 AU, we only reach $$h\sim10^{-7}$$. For your weapon to produce observable changes, you'd need to place it in the enemy star system, which I'm reasonably certain would violate the terms of the treaty!

The alternative, of course, is to use much larger black holes. Unfortunately, because the strain is only linearly proportional to the mass of the black holes, you'd need a supermassive black hole binary ($$M\sim10^6M_{\odot}$$-$$10^9M_{\odot}$$) to produce noticeable changes at distances of a parsec or so, pushing the existing observational and theoretical limits of the supermassive black holes we know. Moreover, these monsters and the accretion disks and fast-moving clouds around them would constitute significant weapons on their own, and I'd bet that it would be extremely hard to control them - even for a civilization of the capacity you describe.

### Miscellaneous notes:

• The power of the Hawking radiation from each black hole is about $$L\sim10^{-31}\text{ W}$$, so it is far from dangerous. Furthermore, they are extremely cool and therefore will only be able to produce extremely low-energy photons, posing no threat whatsoever to any civilization in that sense.

• The gravitational wave emission will not be isotropic, as you might imagine, given that the binary is not spherically symmetric. Therefore, there are ways you could angle the system such that your target receives the maximum emission and you receive the minimum (but, as per our analysis earlier, you're in no danger provided you stay far enough away).

• The effective range of the black holes is much less than 1 AU; for example, at that distance, the maximum strain is $$h\sim10^{-7}$$, optimistically.

• Would it violate the existing terms of the treaty? As the Hawking radiation would be negligible, you're safe on that front; given that you'd have to enter the other system for the weapon to have any effect, I'd argue that attempting to use this as a weapon would indeed violate the clause regarding "gravitational disruption".

• You can show that near coalescence, $$v/c\approx0.7$$. This is because you can show from Kepler's third law that $$v/c\approx R_S^{1/2}/R^{1/2}$$, where $$R$$ is the distance between the centers of the black holes and $$R_S$$ is the Schwarzschild radius of one of the black holes, assuming approximately equal mass. Just before they meet, $$R=2R_S$$, so $$v/c\approx\sqrt{(1/2)}\approx0.71$$.

I'm not sure it matters whether gravity waves make a great weapon given that the sources for those weapons will wreak havoc on anything even remotely close through gravitational disturbances of the solar systems normal orbits.

Gravitational waves are only weakly interacting compared to electromagnetic radiation. However, even weakly interacting particles such as neutrinos can be lethal in sufficient quantities.

I don't have the math to prove anything but they will be one of two scenarios.

1. Gravitational waves are insufficiently strong to do any damage at distances where gravity from the black holes doesn't kill (directly or indirectly). Thus they behave according to the same laws that govern how strong gravity is at a certain distance.
2. The waves do deliver lethal energy at distances outside the black hole's gravity kill zone.

I strongly suspect it is the first situation. If so, then an attack by gravitational waves is equivalent to an attack using black holes.

• When 2 massive objects particularly neutron stars orbiting each other rapidly as they draws closer to each other the gravitational waves will carry away some of its energy like a series of ripples in a pond. When the collision finally occurs it is thought that there will be a burst of gravitational waves carrying lots of energy away mostly from event such as supernova, it will be like a splash with a shockwave! – user6760 Aug 4 '15 at 5:14