Post-Newtonian expansion of a rigidly rotating disc of dust with a constant specific charge

We present an algorithm for obtaining the post-Newtonian expansion of the asymptotically flat solution to the Einstein-Maxwell equations describing a rigidly rotating disc of dust with a constant specific charge. Explicit analytic expressions are calculated up to the eighth order. The results are used for a physical discussion of the extreme relativistic limiting cases. We identify strong evidence for a transition to an extreme Kerr-Newman black hole.