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

TL;DR

This paper develops an algorithm to derive high-order post-Newtonian expansions for a rotating charged dust disc in Einstein-Maxwell theory, providing insights into black hole limits.

Contribution

It introduces a novel algorithm for post-Newtonian expansion of a charged rotating dust disc and computes explicit expressions up to eighth order.

Findings

Evidence for transition to an extreme Kerr-Newman black hole

Explicit eighth-order post-Newtonian expressions

Analysis of relativistic limiting cases

Abstract

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.