Generating solutions to the Einstein–Maxwell equations

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 paper, continuous transformations are considered. Accordingly, originating from the so-called [Formula: see text]-metric, other exact solutions to the E–M equations are recovered and discussed.