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Uniqueness of the Kerr–de Sitter Spacetime as an Algebraically Special Solution in Five Dimensions

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de Freitas, GB 
Godazgar, M 
Reall, HS 


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).



gr-qc, gr-qc, hep-th

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Communications in Mathematical Physics

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Springer Science and Business Media LLC
Science and Technology Facilities Council (ST/J000434/1)
Science and Technology Facilities Council (ST/L000385/1)
Science and Technology Facilities Council (ST/L000636/1)
This work was supported by the European Research Council grant no. ERC-2011-StG 279363-HiDGR. G.B.F. is supported by CAPES grant no. 0252/11-5. M.G. is supported by King’s College, Cambridge.