# Cluster of Black Holes around a Central Point

Within the Star Wars Extended Universe, there is a science base on a small object within a near impenetrable sphere of Black Holes. Is this possible?

The place referenced is called the Maw Installation

• There is a similar reference in the Mass Effect series that has a location nearing the center of the galaxy that is sorrounded by black holes. The race creating and keeping this stable ultimately has control over mass (through element 0, mass effect has an element that controls it's mass based on an electric current flowing through it). Short of this gravitational manipulation, I don't see how it's possible. – Twelfth Oct 17 '14 at 22:32
• For what it's worth, later EU canon indicated that Maw Cluster was an artifical construct left over from the Celestials (constructed by their slave races). As such, all bets are off in-universe as far as what's possible since it's an engineered construct and they could engineer around any problems presented in the existing answers. – user4239 Oct 22 '14 at 18:54

Under the circumstances you describe, my immediate reaction is that it would not be possible. The issue here is that the cluster would be fairly unstable. The black holes would all be mutually attracted to each other, and would soon coalesce into one large black hole - taking the Imperial research center with it.

For this to somehow work, the black holes would have to be in some odd stable orbits around each other. They would have a common barycenter - in this case, the Imperial research center - and would continue circling around it. The tricky part here would be to have them orbit in three dimensions - that is, to not simply have all their orbits in the same plane, but to have orbits at odd angles to each other. Also, there would undoubtedly be gaps between the black holes, which would be undesirable.

The whole setup would seem to be rather unstable, and so I'm inclined to say that this would be impossible.

Let's say that the cluster and the station popped into existence one day. I know, it violates so many laws of physics, but I want to delve into the station's hypothetical downfall, so reality will just have to wait. Anyway, so we have a cluster of black holes in stable orbits. What will happen?

Certain systems, such as binary neutron stars, emit radiation in the form of gravitational waves. A system composed of two black holes orbiting each other should do the same. We can calculate the rate at which their orbits will decay with the formula $$\frac{dr}{dt}=-\frac{64}{5}\frac{G^3}{c^5}\frac{(m_1m_2)(m_1+m_2)}{r^3}$$ where $m_1$ and $m_2$ are the masses and $r$ is the distance between the two black holes. If you imagine the black holes each have a mass of about five solar masses, and are separated by about one kilometer, you can easily do the math and figure out the rate at which the orbit will decay.

Alternatively, we can integrate like so: $$\int_{r_0}^r r'^3dr'=-\int_0^t \frac{64}{5}\frac{G^3}{c^5}(m_1m_2)(m_1+m_2)dt'$$ to find the relationship between the distance between the black holes and time, and calculate how long it will take for the two black holes to meet. This gives you the solution $$r(t)=\sqrt[4]{r_0^4-4\frac{64}{5}\frac{G^3}{c^5}(m_1m_2)(m_1+m_2)t}$$ where $r_0=r(0)$ is the initial radius. The time to coalescence is then $$\tau=r_0^4\left(4\frac{64}{5}\frac{G^3}{c^5}(m_1m_2)(m_1+m_2)\right)^{-1}$$

I'm not sure how this would all work with a system of $n$ black holes, but I would think they would still emit gravitational radiation. Perhaps you could use a modified formula (though I don't know for sure).

Finally, the Imperial research station would have to be in the exact center of the cluster. If it was off by just a bit, it would be pulled towards one side and consumed by a black hole. Perhaps the workers could somehow adjust the station's position, but they would have to be careful to keep it in equilibrium.

• and as soon as one black hole comes too near another then they coalesce and get a new orbit, resulting in eventually a few big black holes – ratchet freak Oct 17 '14 at 7:43
• Globular clusters of stars have been known to contain black holes floating around in them; it's not too far fetched to imagine that a very old globular cluster could have multiple black holes. If the space station doesn't have to be in the center of the cluster, it might be able to safely orbit the galactic core for some period of time on a carefully calculated orbit. The calculations, though, would be... astronomical. – boxcartenant Jul 30 '18 at 23:50

Aside from the problem of instability, which has already been mentioned and is indeed a gigantic problem, I'd like to illustrate another problem.

Everything would be torn apart by gravitational gradients. Yes, technically, you could have an unstable equilibrium where you can place a small object in the middle and it would stay there. you likely want them to be far apart though. But since You want a whole sphere of them, putting them far away either requires a lot of them, or very large one.

To calculate the mass of a black hole from its Schwarzschild radius, you can use the following formula: $\frac{2GM}{c^{2}}$, where G is the gravitational constant, M is the mass of our black hole and c is of course the speed of light. According to Wikipedia, this roughly translates to a 2.95 km radius per solar mass. So lets say we're working with solar mass black holes.

Now, how far do we put those black holes? Well if we have about 60 black holes in a circle, almost touching, they would be in a circle with a radius of about 35 km. To form a sphere of that size, you'd need several hundreds of black holes. I'm not sure where you're getting these, but sure.

We'll focus on just two black holes for now, 70 km apart and circling each other with a small object in the center. If we want to figure out what sort of acceleration that small object is experiencing, we can use the following formula: $G\frac{M}{r^{2}}$ Where G is the gravitational constant again, M the mass of the black hole and r, the distance between the two objects (the small object and the black hole). Filling this out gives us: $6.673\times10^{−11}m^{3}kg^{-1}s^{-2}\frac{1.988\times10^{30}kg}{35000m^{2}}=108293257143 m/s^{2}$, That's quite some acceleration, by Newtonian gravity you'd accelerate to many time the speed of light in less than a second. Of course this doesn't hold, but it gives you an idea of the magnitude of the forces you're facing.

"But the other black hole is just as far away!", I hear you exclaim. That's true. But lets see what the gravitational acceleration looks like a meter further away from this one black hole. $6.673\times10^{−11}m^{3}kg^{-1}s^{-2}\frac{1.988\times10^{30}kg}{35001m^{2}}=108287069222 m/s^{2}$, That looks roughly the same. Let's have a look at the difference $108293257143m/s^{2}-108287069222m/s^{2}=6187921m/s^{2}$. That's not looking to healthy, lets put that in perspective.

If you were to lay out Peter Dinklage with his feet 35 km away from a sun mass black hole and his head 1 m further away (Peter Dinklage is roughly a meter long, right?) the imp would be the size of the mountain (who I am assuming is 3 m tall) in less than a millisecond. His euphoria would be brief however, because he would soon be spaghettified, as would your small object, your science base and everyone in it.