Uniqueness of the Kerr–de Sitter Spacetime as an Algebraically Special Solution in Five Dimensions
de Freitas, GB
Communications in Mathematical Physics
Springer Science and Business Media LLC
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de Freitas, G., Godazgar, M., & Reall, H. (2015). Uniqueness of the Kerr–de Sitter Spacetime as an Algebraically Special Solution in Five Dimensions. Communications in Mathematical Physics, 340 291-323. https://doi.org/10.1007/s00220-015-2447-0
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).
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.
Science and Technology Facilities Council (ST/J000434/1)
Science and Technology Facilities Council (ST/L000385/1)
Science and Technology Facilities Council (ST/L000636/1)
External DOI: https://doi.org/10.1007/s00220-015-2447-0
This record's URL: https://www.repository.cam.ac.uk/handle/1810/249269
Attribution 2.0 UK: England & Wales
Licence URL: http://creativecommons.org/licenses/by/2.0/uk/