Black holes have no-hair so there are uniquely specified by a mass, charge and angular momentum. Imagine a cloud of charged rotating dust. There will be a magnetic field associated with the current of charge that is rotating. As this cloud collapses to form a black hole, how is the magnetic field excluded from the region of the black hole?
These three questions are similar but I think the answers will be different for each one:
What happens to an embedded magnetic field when a black hole is formed from rotating charged dust? It seems to me a rotating charged black hole must have a dipole magnetic field. But the strength of the dipole field seems like an extra parameter that black holes are forbidden by the no-hair theorem.
If a magnetic monopole falls into a schwarzchild black hole, what happens to the magnetic field? Here there would be only radial magnetic field lines leaving from the event horizon to infinity. So if magnetic charge is counted as charge this should be no problem. But if the black hole were rotating wouldn't that produce an electric dipole field?
When a neutral star with a magnetic field collapses to form a black hole, what happens to the magnetic field? Here there is no charge so how can there be a magnetic field associated with a black hole? That would definitely violate the no-hair theorem.