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Generalized Weyl solutions
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It was shown by Weyl that the general static axisymmetric solution of the vacuum Einstein equations in four dimensions is given in terms of a single axisymmetric solution of the Laplace equation in three-dimensional flat space. Weyls construction is generalized here to arbitrary dimension D>~4. The general solution of the D-dimensional vacuum Einstein equations that admits D-2 orthogonal commuting non-null Killing vector fields is given either in terms of D-3 independent axisymmetric solutions of Laplaces equation in three-dimensional flat space or by D-4 independent solutions of Laplaces equation in two-dimensional flat space. Explicit examples of new solutions are given. These include a five-dimensional asymptotically flat black ring with an event horizon of topology S1S2 held in equilibrium by a conical singularity in the form of a disk.
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EMPARAN GARCÍA DE SALAZAR, Roberto a., REALL, Harvey s.. Generalized Weyl solutions. _Physical Review D_. 2002. Vol. 65, núm. 8, pàgs. 084025-1-084025-26. [consulta: 21 de gener de 2026]. ISSN: 0556-2821. [Disponible a: https://hdl.handle.net/2445/12373]