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If I were somehow able to create two negatively charged black holes, could they repel each other? Or does gravity always win?

Ron Dippold
San Diego, California, US

Gravity wins. Which is strange, because gravity is by far the weakest major force – the gravitational force between an electron and positron is 10⁴³ weaker than the electromagnetic force between them. But while charged black holes are certainly theoretically possible, a negatively charged black hole will preferentially attract positively charged particles and repel negatively charged ones. This then increases its mass and lowers its negative charge. The takeaway is that it is quite hard to keep a black hole too positively or negatively charged for long.

What if you could somehow create two 1-kilogram black holes in a perfect vacuum with zero other forces? The particle physics laboratory CERN in Switzerland would like to talk to you. But there is another limit – the extremal charge for a black hole is the amount of charge it can have before the electromagnetic forces trying to tear it apart balance the gravitational forces holding it together, creating an event horizon. If it had more charge than that, the interior of the black hole would be pushed beyond the event horizon, and as far as we know, that’s impossible.

Two negatively charged black holes attracting or repelling depends on the distance between them

This also holds for the forces between two black holes. Neither can exceed the extremal charge, and if they are both at the extremal charge, the best you can do is have the electromagnetic repulsion between them balance their gravitational attraction. It doesn’t matter how big they are; even if they were each 1 trillion kilograms, this would still be a limit.

And, as noted, it is very hard to keep a black hole from losing charge and gaining mass. It is possible that the extremal charge limit is incorrect, because black holes are weird. But barring that, eventually, gravity wins. That, or else both black holes disintegrate from Hawking radiation.

Philip Lillies
Ottawa, Canada

This is a very interesting question, and amazingly, I think I know the answer. At some specific distance, the black holes would neither repel nor attract. But if they just got a little closer together, they would attract each other (gravity would win). If they got a little farther apart, they would repel each other (negative charge would win).

The reason why is that gravity, unlike electrical force, is nonlinear. Gravity works by bending space-time, which adds energy, which causes more bending. In other words, gravity gravitates. Near massive bodies like the sun – or black holes – this effect becomes more noticeable, which is why Mercury’s orbit slowly shifts over time. So, whether two negatively charged black holes would attract or repel depends on the distance between them.

Eric Kvaalen
Les Essarts-le-Roi, France

Certainly, if they have enough charge, two black holes will repel each other. Specifically, if they both have a ratio of charge to mass greater than 86.2 nanocoulombs per tonne or, more generally, if the geometric mean of this ratio for the two black holes is greater than that value. That’s equivalent to 538,000 electrons per gram.

But the question is whether it is possible to create such black holes. If a non-conducting ball has a constant ratio of charge density to mass density throughout that is greater than 86.2 nanocoulombs per tonne, then it won’t collapse into a black hole – it will expand. If a ball that does conduct charge, such as a star, has such a high charge, the charge will migrate to the surface, and the outer shell will be accelerated away from the rest of the star.

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