  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.
