When a neutral star with a magnetic field collapses to form a black hole, what happens to the magnetic field? By the no-hair theorem, black holes are only characterized by mass, charge and angular momentum.  If the star is neutral, the black hole will have only mass and angular momentum - and therefore it cannot have a magnetic dipole field.  Where did it go?

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.

 A: There is a test of the collapse of a magnetized neutron star (case 3) in this preprint: http://arxiv.org/abs/arXiv:1208.3487.
Here is some of the text and figures from that paper that describe how the magnetic field is expelled:


  
*Magnetized Collapse to a Black Hole
  
  
  Our final and most comprehensive test is represented by the collapse
  to a BH of a magnetized nonrotating star. This is more than a purely
  numerical test as it simulates a process that is expected to take
  place in astrophysically realistic conditions, such as those
  accompanying the merger of a binary system of magnetized neutron stars
  [26, 27], or of an accreting magnetized neutron star. The interest in
  this process lays in that the collapse will not only be a strong
  source of gravitational waves, but also of electromagnetic radiation,
  that could be potentially detectable (either directly or as processed
  signal). The magnetized plasma and electromagnetic fields that
  surround the star, in fact, will react dynamically to the rapidly
  changing and strong gravitational fields of the collapsing star and
  respond by emitting electromagnetic radiation. Of course, no
  gravitational waves can be emitted in the case considered here of a
  nonrotating star, but we can nevertheless explore with unprecedented
  accuracy the electromagnetic emission and assess, in particular, the
  efficiency of the process and thus estimate how much of the available
  binding energy is actually radiated in electromagnetic waves. Our
  setup also allows us to investigate the dynamics of the
  electromagnetic fields once a BH is formed and hence to assess the
  validity of the no-hair theorem, which predicts the exponential decay
  of any electromagnetic field in terms of Quasi Normal Mode (QNM)
  emission from the BH.
...
As the collapse proceeds, the restmass density in the center and the
  curvature of the spacetime increase until an appararent horizon is
  found at t = 0.57 ms and is marked with a thin red line in Fig. 12. 
  As the stellar matter is accreted onto the BH (the rest-mass outside
  the horizon $M_{b, out} = 0$ is zero by $t \geq 0.62$ ms), the external magnetic
  field which was anchored on the stellar surface becomes disconnected,
  forming closed magneticfield loopswhich carry away the electromagnetic
  energy in the form of dipolar radiation. This process, which has been
  described through a simplified non-relativistic analytical model in
  Ref. [52], predicts the presence of regions where |E| > |B| as the
  toroidal electric field propagates outwards as a wave. This process
  can be observed very clearly in Fig. 13, which displays the same three
  bottom panels of Fig. 12 on a smaller scale of only 15 km to highlight
  the dynamics near the horizon. In particular, it is now very clear
  that a closed set of magnetic field lines is built just outside the
  horizon at t = 1.0 ms, that is radiated away. Note also that our
  choice of gauges (which are the same used in [61]) allows us to model
  without problems also the solution inside the apparent horizon. While
  the left panel of Fig. 13 shows thatmost of the rest-mass is
  dissipated away already by t = 0.65 ms (see discussion in [62] about
  why this happens), some of the matter remains on the grid near the
  singularity, anchoring there the magnetic field which slowly evolves
  as shown in the middle and right panels.
  


