Generalized Weyl solutions
Oct, 200149 pages
Published in:
- Phys.Rev.D 65 (2002) 084025
e-Print:
- hep-th/0110258 [hep-th]
Report number:
- CERN-TH-2001-293
Citations per year
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 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.- 04.70.Bw
- 04.50.+h
- 04.20.Jb
- Einstein equation: solution
- differential equations: Laplace
- any-dimensional
- symmetry: axial
- string
- Kaluza-Klein model
- space-time
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