Given a Schwarzschild BH. A neutron fall into the BH. The neutron having non zero magnetic moment will carry a magnetic field B with it. How do I describe the new system, on which parameters will the metric depend? In term of classical GR, Kerr Newman solution provides a B in term of the charge Q and angular momentum J (and the no hair theorem is satisfied). I see a paradox might emerge. 1) If the B from the added neutron can be described as a Kerr Newman solution, then I don't know how to explain charge conservation. For both the initial systems schwarzschild BH and neutron, Q is zero. 2) If I have instead a solution for the metric with zero Q and J, the metric will have to depend on the intrinsic magnetic moment. This would violate the no hair theorem Another way to state the problem is the following. Consider a macroscopic neutral magnet. Somehow it shirks to form a BH. Again, which will be the parameter in the metric? If Q and J, then I cannot explain Q conservation. If the magnetic moment, then no hair theorem is violated. I have been thinking about this for a while, maybe classical GR is not enough.