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

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

2010-02-02

arxiv.org/abs/1002.0490v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LaTex, 22 pages, 9 figures

Scientific paper

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 $CP^2$'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.

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