Gauge-Theoretical Method in Solving Zero-curvature Equations II--Non-Weyl Class Solutions of the Static Einstein-Maxwell Equations

TL;DR

This paper applies a gauge-theoretical method to find new static Einstein-Maxwell solutions, including non-Weyl class cases, revealing configurations with finite Dirac strings between magnetic charges.

Contribution

It extends previous work by deriving non-Weyl class solutions for static Einstein-Maxwell equations, including a novel magnetostatic solution with finite Dirac string.

Findings

Reproduces Bonnor's electrostatic solution from 1979.

Introduces a magnetostatic solution with two magnetic charges.

Finds a configuration with a finite Dirac string between charges.

Abstract

The gauge-theoretical method introduced in our previous paper is applied to solve the axisymmetric and static Einstein-Maxwell equations. We obtain the solutions of the non-Weyl class, where the gravitational and electric or magnetic potentials are not functionally related. In the electrostatic case, we show that the obtained solution coincides with the solution given by Bonnor in 1979. In the magnetostatic case, we present a solution describing the gravitational field created by two magnetically charged masses. In this solution, we present a case in which the Dirac string does not stretch to spatial infinity but lies between the magnetically charged masses.