Generating solutions to the Einstein-Maxwell equations

摘要

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 gamma(A)-metric, other exact solutions to the E-M equations are recovered and discussed.