# Description of magnetic field in black holes

1. May 22, 2008

### Srr

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.