Lets think about a point charge is falling into black hole. I know that electric field can be get out from the black hole. Then how about magnetic field? What happens to magnetic field since the charge starts to fall into the black hole? Suppose that black hole has no charge, no angular velocity.
If the hole has no angular momentum and the particle falls in radially, then the magnetic field goes to zero as it approaches the horizon.
If the particle falls in non-radially, giving the hole some angular momentum, or the hole already had angular momentum, you end up with a hole that has a magnetic field.
The first paragraph is an educated guess, based in general on the no-hair theorems and more specifically on an exact solution of what happens to the electrostatic field of a point charge as it is slowly lowered into a black hole. (It becomes centered on the hole, so that the charge’s field provides no hair.) I am not aware of an exact solution for the electric and magnetic fields of an infalling charge, but I am reasonably confident that a perturbative calculation would show the magnetic field dying away during radial infall, because a non-rotating hole cannot have a magnetic field.