Generating Solutions to the Einstein - Maxwell Equations

TL;DR

This paper derives solutions to the Einstein-Maxwell equations in curved spacetime with symmetries, using a potential transformation approach to generate new exact solutions from known seed solutions.

Contribution

It introduces a method to generate new Einstein-Maxwell solutions via continuous transformations of potentials based on a Lagrangian framework.

Findings

Recovered new exact solutions from the γ_A-metric

Demonstrated the transformation of seed solutions into novel solutions

Provided a systematic approach for solution generation in Einstein-Maxwell theory

Abstract

The Einstein-Maxwell (E-M) equations in a curved spacetime that admits at least one Killing vector are derived, from a Lagrangian density adapted to symmetries. In this context, an auxiliary space of potentials is introduced, in which, the set of potentials associated to an original (seed) solution of the E-M equations are transformed to a new set, either by continuous transformations or by discrete transformations. In this article, continuous transformations are considered. Accordingly, originating from the so-called $\gamma_A$-metric, other exact solutions to the E-M equations are recovered and discussed.