Generalized Weyl solutions

Oct, 2001
49 pages
Published in:
  • Phys.Rev.D 65 (2002) 084025
e-Print:
Report number:
  • CERN-TH-2001-293

Citations per year

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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 D4D\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.
  • 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