In this question, the general consensus is that a charged black hole does have an associated electric field, due to the charges that have at some point gone inside (since their retarded potentials existed before the black hole did).
Now, if the black hole is also rotating, then the inner charge would also be rotating, producing a current loop that one could a priori assimilate to that of a circular wire carrying a current. And therefore, it should have a magnetic field.
Does the argument presented in the answer to the electric field question apply here? After all, while the charges existed before the black hole and therefore their contribution also did, they weren't necessarily forming a current that would have an associated magnetic field.
