  We discuss the limit of vanishing $G$ (Newton's constant of universal
gravitation) of the maximal analytically extended Kerr--Newman electrovacuum
spacetimes {represented in Boyer--Lindquist coordinates}. We investigate the
topologically nontrivial spacetime emerging in this limit and show that it
consists of two copies of flat Minkowski spacetime glued at a timelike solid
cylinder. As $G\to 0$, the electromagnetic fields of the Kerr-Newman spacetimes
converge to nontrivial solutions of Maxwell's equations on this background
spacetime. We show how to obtain these fields by solving Maxwell's equations
with singular sources supported only on a circle in a spacelike slice of the
spacetime. These sources do not suffer from any of the pathologies that plague
the alternate sources found in previous attempts to interpret the Kerr--Newman
fields on the topologically simple Minkowski spacetime. We characterize the
singular behavior of these sources and prove that the Kerr-Newman electrostatic
potential and magnetic stream function are the unique solutions of the Maxwell
equations among all functions that have the same blow-up behavior at the ring
singularity.
