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 ultrarelativistic 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 "hyperextreme" Kerr-Newman solution with the same gravitational mass, angular momentum and charge.

Continuous sequences of asymptotically flat solutions to the Einstein-Maxwell equations describing regular equilibrium configurations of ordinary matter can reach a black hole limit. For a distant observer, the spacetime becomes more and more indistinguishable from the metric of an extreme Kerr-Newman black hole outside the horizon when approaching the limit. From an internal perspective, a still regular but non-asymptotically flat spacetime with the extreme Kerr-Newman near-horizon geometry at spatial infinity forms at the limit. Interesting special cases are sequences of Papapetrou-Majumdar distributions of electrically counterpoised dust leading to extreme Reissner-Nordström black holes and sequences of rotating uncharged fluid bodies leading to extreme Kerr black holes.

We calculated the dimensionless gyromagnetic ratio ("g-factor") of self-gravitating, uniformly rotating disks of dust with a constant specific charge . These disk solutions to the Einstein-Maxwell equations depend on and a "relativity parameter" γ (0 < γ ≤ 1) up to a scaling parameter. Accordingly, the g-factor is a function g = g(γ, ). The Newtonian limit is characterized by γ 1, whereas γ → 1 leads to a black-hole limit. The g-factor, for all , approaches the values g = 1 as γ → 0 and g = 2 as γ → 1.