On a zero-gravity limit of the Kerr-Newman spacetimes and their electromagnetic fields

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 M 0 emerging in this limit and show that it consists of two copies of flat Minkowski spacetime cross-linked at a timelike solid cylinder (spacelike 2-disk × timelike R). As G → 0, the electromagnetic fields of the Kerr-Newman spacetimes converge to nontrivial solutions of Maxwell's equations on this background spacetime M 0. 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 M 0. 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 scalar potential are the unique solutions of the Maxwell equations among all functions that have the same blow-up behavior at the ring singularity.