Further restrictions on the topology of stationary black holes in five dimensions

Abstract

We place further restriction on the possible topology of stationary asymptotically flat vacuum black holes in 5 spacetime dimensions. We prove that the horizon manifold can be either a connected sum of Lens spaces and "handles" $S^1\times S^2$, or the quotient of $S^3$ by certain finite groups of isometries (with no "handles"). The resulting horizon topologies include Prism manifolds and quotients of the Poincare homology sphere. We also show that the topology of the domain of outer communication is a cartesian product of the time direction with a finite connected sum of ${\mathbb{R}}^4,S^2\times S^2$'s and $C{P}^2$'s, minus the black hole itself. We do not assume the existence of any Killing vector beside the asymptotically timelike one required by definition for stationarity.

LaTex, 22 pages, 9 figures

References in corpus (8)

• A Higher Dimensional Stationary Rotating Black Hole Must be Axisymmetric
• Uniqueness theorem for 5-dimensional black holes with two axial Killing fields
• Symmetries of Higher Dimensional Black Holes
• New Horizons for Black Holes and Branes
• On the `Stationary Implies Axisymmetric' Theorem for Extremal Black Holes in Higher Dimensions
• Topological censorship for Kaluza-Klein space-times
• Domain Structure of Black Hole Space-Times
• Topology Change of Black Holes

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