Communications in Mathematical Physics

, Volume 283, Issue 3, pp 749–768 | Cite as

Uniqueness Theorem for 5-Dimensional Black Holes with Two Axial Killing Fields

  • Stefan HollandsEmail author
  • Stoytcho Yazadjiev


We show that two stationary, asymptotically flat vacuum black holes in 5 dimensions with two commuting axial symmetries are identical if and only if their masses, angular momenta, and their “interval structures” coincide. We also show that the horizon must be topologically either a 3-sphere, a ring, or a Lens-space. Our argument is a generalization of constructions of Morisawa and Ida (based in turn on key work of Maison) who considered the spherical case, combined with basic arguments concerning the nature of the factor manifold of symmetry orbits.


Black Hole Black Hole Solution Isometry Group Orbit Space Tubular Neighborhood 
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© Springer-Verlag 2008

Authors and Affiliations

  1. 1.School of MathematicsCardiff UniversityWalesUK
  2. 2.Department of Theoretical Physics, Faculty of PhysicsSofia UniversitySofiaBulgaria

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