Robert Debever

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

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.

Riemannian-Maxwellian invertible structures in general relativity

It is shown that a space-time admitting a nonsingular 2-form satisfying the source-free Maxwell equations and a Lorentzian involution under which the 2-form and the exterior derivative of a related 2-form are skew invariant while the trace-free Ricci tensor and the covariant derivative of the involution itself are invariant possesses locally an invertible 2-parameter Abelian isometry group with nonsingular orbits.

A single expression for the general solution of Einstein's vacuum and electrovac field equations with cosmological constant for Petrov type D admitting a non-singular aligned Maxwell field

Abstract We present a single expression for the general solution of Einsteins vacuum and electrovac field equations with cosmological constant for Petrov type D admitting a non-singular aligned Maxwell field satisfying the generalized Goldberg-Sachs theorem from which all the particular cases until the present known in partial versions may be deduced.

Empty spaces and perfect fluids with homothetic transformation

A class of Lorentzian metrics in one variable that admits homothetic transformation is introduced. Solutions of Einsteins empty space equations are presented. The case of perfect fluids is discussed.