A new special class of Petrov type D vacuum space-times in dimension five
Alfonso Garc\'ia-Parrado G\'omez-Lobo, Lode Wylleman
TL;DR
This paper extends the Newman-Penrose and Geroch-Held-Penrose formalisms to five dimensions to classify a special class of Petrov type D vacuum space-times with isotropic Riemann tensors in a specific plane.
Contribution
It introduces a novel classification of Petrov type D vacuum solutions in five dimensions using extended formalisms.
Findings
Classified all Petrov type D vacuum solutions with specified isotropy conditions.
Extended formalism applicable to higher-dimensional space-times.
Provides invariant characterization of these solutions.
Abstract
Using extensions of the Newman-Penrose and Geroch-Held-Penrose formalisms to five dimensions, we invariantly classify all Petrov type vacuum solutions for which the Riemann tensor is isotropic in a plane orthogonal to a pair of Weyl alligned null directions
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