Algebraically special Einstein-Maxwell fields

TL;DR

This paper uses the Geroch-Held-Penrose formalism to analyze algebraically special Einstein-Maxwell fields, providing new invariant characterizations of certain metrics and clarifying the geometric properties of class D solutions with a cosmological constant.

Contribution

It offers a novel invariant characterization of specific Einstein-Maxwell solutions and links their algebraic properties to geometric behaviors like shear-free and geodesic vectors.

Findings

New invariant characterizations of Garcia-Plebanski and Plebanski-Hacyan metrics.

Double alignment of class D metrics is equivalent to shear-free, geodesic vectors.

Clarification of geometric properties of Einstein-Maxwell fields with cosmological constant.

Abstract

The Geroch-Held-Penrose formalism is used to re-analyse algebraically special non-null Einstein-Maxwell fields, aligned as well as non-aligned, in the presence of a possible non-vanishing cosmological constant. A new invariant characterisation is given of the Garcia-Plebanski and Plebanski-Hacyan metrics within the family of aligned solutions and of the Griffiths metrics within the family of the non-aligned solutions. As a corollary also the double alignment of the Debever-McLenaghan 'class D' metrics with non-vanishing cosmological constant is shown to be equivalent with the shear-free and geodesic behaviour of their Debever-Penrose vectors.