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

Abstract

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 M0 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 M0. 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 M0. 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.