  Investigating the rigidly rotating disc of dust with constant specific
charge, we find that it leads to an extreme Kerr-Newman black hole in the
ultra-relativistic limit. A necessary and sufficient condition for a black hole
limit is, that the electric potential in the co-rotating frame is constant on
the disc. In that case certain other relations follow. These relations are
reviewed with a highly accurate post-Newtonian expansion.
  Remarkably it is possible to survey the leading order behaviour close to the
black hole limit with the post-Newtonian expansion. We find that the disc
solution close to that limit can be approximated very well by a
"hyper\-extreme" Kerr-Newman solution with the same gravitational mass, angular
momentum and charge.
