Generalized Weyl Solutions
نویسندگان
چکیده
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. Weyl’s 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 Laplace’s equation in three-dimensional flat space or by D− 4 independent solutions of Laplace’s 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 S1×S2 held in equilibrium by a conical singularity in the form of a disc. Also at Departamento de F́ısica Teórica, Universidad del Páıs Vasco, E-48080, Bilbao, Spain.
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