A new special class of Petrov type D vacuum space-times in dimension five

Abstract

Using extensions of the Newman-Penrose and Geroch-Held-Penrose formalisms to five dimensions, we invariantly classify all Petrov type $D$ vacuum solutions for which the Riemann tensor is isotropic in a plane orthogonal to a pair of Weyl alligned null directions

4 pages, 1 table, no figures. Contribution to the proceedings of the Spanish Relativity Meeting 2010 held in Granada (Spain)

References in corpus (4)

• Generalization of the Geroch-Held-Penrose formalism to higher dimensions
• Type D Einstein spacetimes in higher dimensions
• A higher-dimensional generalization of the geodesic part of the Goldberg-Sachs theorem
• Petrov D vacuum spaces revisited: Identities and Invariant Classification

Cited by in corpus (5)

• On a five-dimensional version of the Goldberg-Sachs theorem
• The complex Goldberg-Sachs theorem in higher dimensions
• Refinements of the Weyl tensor classification in five dimensions
• On the uniqueness of the Myers-Perry spacetime as a type II(D) solution in six dimensions
• On the uniqueness of the Kerr-(A)dS metric as a type II(D) solution in six dimensions