On algebraically special vacuum spacetimes in five dimensions
arXiv:1211.5957 · doi:10.1088/0264-9381/30/5/055004
Abstract
Vacuum solutions admitting a hypersurface-orthogonal repeated principal null direction are an important class of 4d algebraically special spacetimes. We investigate the 5d analogues of such solutions: vacuum spacetimes admitting a hypersurface-orthogonal multiple Weyl aligned null direction (WAND). Such spacetimes fall into 4 families determined by the rank of the 3X3 matrix that defines the expansion and shear of the multiple WAND. The rank 3 and rank 0 cases have been studied previously. We investigate the 2 remaining families. We show how to define coordinates which lead to a considerable simplification of the Einstein equation with cosmological constant. The rank 2 case gives warped product and Kaluza-Klein versions of the 4d Robinson-Trautman solutions as well as some new solutions. The rank 1 case gives product, or analytically continued Schwarzschild, spacetimes.
25 pages. v2: typos corrected
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Cited by in corpus (7)
- Extended Kerr-Schild spacetimes: General properties and some explicit examples
- On the Goldberg-Sachs theorem in higher dimensions in the non-twisting case
- On the uniqueness of the Myers-Perry spacetime as a type II(D) solution in six dimensions
- On higher dimensional Einstein spacetimes with a non-degenerate double Weyl aligned null direction
- 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