On the black hole limit of rotating discs of charged dust

Abstract

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 ‘hyperextreme’ Kerr–Newman solution with the same gravitational mass, angular momentum and charge.