Exhaustive integration and a single expression for the general solution of the type <i>D</i> vacuum and electrovac field equations with cosmological constant for a nonsingular aligned Maxwell field

Abstract

We present an exhaustive integration of the type D vacuum and electrovac field equations with cosmological constant admitting a nonsingular aligned Maxwell field satisfying the generalized Goldberg–Sachs theorem. We derive a single expression for the general solution from which one may obtain all particular cases known until now in partial versions. We also investigate in detail the separability properties of the Hamilton–Jacobi equation for the charged particle orbits and of the Klein–Gordon equation for a massive charged spin-zero test particle and their corresponding Killing tensors.