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

TL;DR

This paper explores the zero-gravity limit of Kerr-Newman spacetimes, revealing a topologically nontrivial background and deriving electromagnetic fields from singular sources on a complex spacetime structure.

Contribution

It introduces a novel topologically nontrivial spacetime emerging in the zero-G limit and constructs electromagnetic fields from singular sources without previous pathologies.

Findings

The zero-G limit results in a spacetime with two Minkowski copies glued at a cylinder.

Electromagnetic fields converge to solutions of Maxwell's equations with singular sources.

Unique solutions are characterized by their behavior at the ring singularity.

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 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.