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Twisting algebraically special solutions in five dimensions

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Godazgar, M 
Reall, HS 


We determine the general form of the solutions of the five-dimensional vacuum Einstein equations with cosmological constant for which (i) the Weyl tensor is everywhere type II or more special in the null alignment classification of Coley et al., and (ii) the 3×3 matrix encoding the expansion, shear and twist of the aligned null direction has rank 2. The dependence of the solution on 2 coordinates is determined explicitly, so the Einstein equation reduces to PDEs in the 3 remaining coordinates, just as for four-dimensional algebraically special solutions. The solutions fall into several families. One of these consists of warped products of four-dimensional algebraically special solutions. The others are new.



algebraic classification, einstein solutions, higher dimensions

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Classical and Quantum Gravity

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IOP Publishing
Science and Technology Facilities Council (ST/L000636/1)
European Research Council (279363)
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.