Charged axially symmetric exponential metric: Exact solutions to the Einstein-Maxwell equations

Abstract

We construct and analyze charged and magnetized extensions of the axially symmetric exponential metric, that is known as the Curzon-Chazy spacetime (CCS) within the Weyl class. Working within the Einstein-Maxwell framework, we first derive an exact charged axially symmetric exponential metric by directly solving the coupled field equations for a dyonic monopole configuration. The solution is shown to reduce smoothly to the vacuum CCS in the neutral limit and to the extremal Reissner-Nordström spacetime in a special parameter regime. We then rederive the same charged geometry using the Harrison transformation in the Ernst formalism, establishing the equivalence between the direct and solution-generating approaches. Subsequently, we apply the magnetic Harrison transformation to obtain a Melvin-type magnetized deformation of the spacetime. Finally, by implementing the Ehlers transformation, we generate a stationary but nonrotating swirling geometry endowed with a nonvanishing NUT charge, which we identify invariantly via the Komar dual mass. A further magnetic Harrison transformation yields a magnetized swirling (NUT-type) spacetime. These results demonstrate how electric, magnetic, and gravitomagnetic charges arise systematically from the CCS through exact solution-generating techniques.