Uniqueness of the Kerr-de Sitter spacetime as an algebraically special solution in five dimensions
Freitas, Gabriel Bernardi de
Communications in Mathematical Physics
MetadataShow full item record
Freitas, G. B. d., 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., and (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.
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/