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Uniqueness of the Kerr-de Sitter spacetime as an algebraically special solution in five dimensions

We determine the most general solution of the five-dimensional vacuum Einstein equation, allowing for a cosmological constant, with (i) a Weyl tensor that is type II or more special in the classification of Coley et al., (ii) a non-degenerate "optical matrix" encoding the expansion, rotation and shear of the aligned null direction. The solution is specified by three parameters. It is locally isometric to the 5d Kerr-de Sitter solution, or related to this solution by analytic continuation or taking a limit. This is in contrast with four dimensions, where there exist infinitely many solutions with properties (i) and (ii).

preprint2015arXivOpen access
Gabriel Bernardi de FreitasMahdi GodazgarHarvey S. Reall
gr-qchep-th
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Gabriel Bernardi de FreitasMahdi GodazgarHarvey S. Reall

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