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 $CP^2$'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.
 Publication:

Annales Henri Poincaré
 Pub Date:
 March 2011
 DOI:
 10.1007/s0002301100792
 arXiv:
 arXiv:1002.0490
 Bibcode:
 2011AnHP...12..279H
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 LaTex, 22 pages, 9 figures