Algebraically special Einstein-Maxwell fields

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.

11 pages, changed title, added two tree diagrams representing the results; minor corrections

Cited by in corpus (6)

• New class of rotating charged black holes with nonaligned electromagnetic field
• Revisiting black holes of algebraic type D with a cosmological constant
• Black holes of type D revisited: relating their various metric forms
• Non-aligned Einstein-Maxwell Robinson-Trautman fields of Petrov type D
• Non-expanding Plebanski-Demianski space-times
• A new class of non-aligned Einstein-Maxwell solutions with a geodesic, shearfree and non-expanding multiple Debever-Penrose vector