Generalized Weyl Solutions

Details Generalized Weyl Solutions Generalized Weyl Solutions

2001-10-29

arxiv.org/abs/hep-th/0110258v2

Phys.Rev. D65 (2002) 084025

Physics

High Energy Physics

High Energy Physics - Theory

50 pages, 10 figures; v2: minor improvements

Scientific paper

10.1103/PhysRevD.65.084025

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 $D\ge 4$. 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 S^1 x S^2 held in equilibrium by a conical singularity in the form of a disc.

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