Twisting algebraically special solutions in five dimensions

Abstract

We determine the general form of the solutions of the five-dimensional vacuum Einstein equations with cosmological constant for which (i) the Weyl tensor is everywhere type II or more special in the null alignment classification of Coley et al., and (ii) the $3\times 3$ matrix encoding the expansion, shear and twist of the aligned null direction has rank 2. The dependence of the solution on 2 coordinates is determined explicitly, so the Einstein equation reduces to PDEs in the 3 remaining coordinates, just as for four-dimensional algebraically special solutions. The solutions fall into several families. One of these consists of warped products of four-dimensional algebraically special solutions. The others are new.

39 pages plus appendix

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• Kundt Spacetimes
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• Type D Einstein spacetimes in higher dimensions
• General Kundt spacetimes in higher dimensions
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Cited by in corpus (6)

• Classification of Kerr-de Sitter-like spacetimes with conformally flat $\mathcal{I}$ in all dimensions
• On the uniqueness of the Myers-Perry spacetime as a type II(D) solution in six dimensions
• Covariant classification of conformal Killing vectors of locally conformally flat $n$-manifolds with an application to Kerr-de Sitter
• Spacetimes of Weyl and Ricci type N in higher dimensions
• On the uniqueness of the Kerr-(A)dS metric as a type II(D) solution in six dimensions
• On type II(D) Einstein spacetimes in six dimensions