Emparan García de Salazar, Roberto A.Reall, Harvey S.2010-05-062010-05-0620020556-2821https://hdl.handle.net/2445/12373It 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.26 p.application/pdfeng(c) The American Physical Society, 2002Relativitat general (Física)Teories del camp unificatGravitacióSolucions numèriquesTeoria de Kaluza-KleinSolucions numèriquesGeneral relativity (Physics)Unified field theoriesGravitationKaluza-Klein theoriesNumerical solutionsinfo:eu-repo/semantics/article510719info:eu-repo/semantics/openAccess