Abstract
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 The general solution of the D-dimensional vacuum Einstein equations that admits orthogonal commuting non-null Killing vector fields is given either in terms of independent axisymmetric solutions of Laplace’s equation in three-dimensional flat space or by 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 held in equilibrium by a conical singularity in the form of a disk.
- Received 8 November 2001
DOI:https://doi.org/10.1103/PhysRevD.65.084025
©2002 American Physical Society