Topology Changing Process of Coalescing Black Holes on Eguchi-Hanson Space

We numerically study the event horizons of two kinds of five-dimensional coalescing black hole solutions with different asymptotic structures: the five-dimensional Kastor-Traschen solution (5DKT) and the coalescing black hole solution on Eguchi-Hanson space (CBEH). Topologies of the spatial infinity are ${\rm S}^3$ and $L(2;1)={\rm S}^3/{\mathbb Z}_2$, respectively. We show that the crease sets of event horizons are topologically ${\rm R}^1$ in 5DKT and ${\rm R}^1\times {\rm S}^1$ in CBEH, respectively. If we choose the time slices which respect space-time symmetry, the first contact points of the coalescing process is a point in the 5DKT case but a ${\rm S}^1$ in the CBEH case. We also find that in CBEH, time slices can be chosen so that a black ring with ${\rm S}^1\times {\rm S}^2$ topology can be also formed during a certain intermediate period unlike the 5DKT.