On the black hole limit of rotating discs of charged dust

TL;DR

This paper demonstrates that a rotating disc of charged dust approaches an extreme Kerr-Newman black hole in the ultra-relativistic limit, with the electric potential's constancy being key to this transition.

Contribution

It establishes the conditions under which a rotating charged dust disc converges to a Kerr-Newman black hole, and uses post-Newtonian expansion to analyze the near-horizon behavior.

Findings

Disc approaches extreme Kerr-Newman black hole in ultra-relativistic limit

Electric potential constant on the disc is necessary and sufficient for black hole limit

Post-Newtonian expansion accurately describes near-limit behavior

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 "hyper\-extreme" Kerr-Newman solution with the same gravitational mass, angular momentum and charge.