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 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.

25 pages; accepted for publication in IJMP D

References in corpus (1)

• Generating Solutions to the Einstein Field Equations

Cited by in corpus (1)

• On a New Formulation of Vacuum Axisymmetric Solutions of general Relativity