Initial Data for Black Holes and Black Strings in 5d

Abstract

We explore time-symmetric hypersurfaces containing apparent horizons of black objects in a 5d spacetime with one coordinate compactified on a circle. We find a phase transition within the family of such hypersurfaces: the horizon has different topology for different parameters. The topology varies from $S^3$ to $S^2\times S^1$. This phase transition is discontinuous -- the topology of the horizon changes abruptly. We explore the behavior around the critical point and present a possible phase diagram.

4 pp, 3 figs. v3: Discussion extended including know variouse choices of the source. The value of ${\zeta }_c$, errors and typos are corrected. Conclusions clarified but ain't changed. More references added. Accepted for publication in PRL