Dyonic black holes: The theory of two electromagnetic potentials

TL;DR

This paper advocates for using two electromagnetic potentials to accurately describe dyonic black holes, demonstrating that the magnetic monopole field is correctly represented by the dual potential, and clarifying the physical irrelevance of the Dirac string.

Contribution

It introduces a framework with two electromagnetic potentials for dyonic black holes, resolving issues related to the Dirac string and providing consistent energy-momentum tensor formulations.

Findings

The magnetic monopole field is described by the dual potential's $t$-component.

The Dirac string is a mathematical artifact with no physical content.

Different energy-momentum tensor forms affect the Dirac string's association with charges.

Abstract

In the present paper we argue that the dyonic black hole spacetimes must be studied within the theory of two electromagnetic potentials, and we use the dyonic Reissner-Nordstr\"om solution to demonstrate that the field of the monopole magnetic charge is correctly described by the $t$-component of the dual electromagnetic potential. As a result, the Dirac string associated with the $\varphi$-component of the usual electromagnetic 4-potential becomes just a mathematical object, without any physical content, that arises in some calculations when one employs unsymmetrical representations of the electromagnetic field. We use three different, though equivalent, forms of the electromagnetic energy-momentum tensor to calculate the Komar mass of the Reissner-Nordstr\"om black hole, and in one case the Dirac string is linked to the magnetic charge, in another to the electric charge, while the third, symmetrical case, is string-free.