Black holes have no hair, meaning they cannot support complicated things like magnetic field lines. If I disconnect a light bulb out of a lamp and I hold it in my hand, in principle, absolute basic electricity magnetism, no relativity, no black holes, nothing fancy. So if I wave a magnet around strongly enough, I will light up that light bulb. And the earth has such a magnetic field neutron stars, a very big magnetic field, black holes. Exactly. The formally proved cannot support the hair of magnetic fields, meaning they just can't have them. It's one of these things that I learned as a student, but always never understood.

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