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

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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 S³ and L(2;1)= S³/Z₂, respectively. We show that the crease sets of event horizons are topologically R¹ in 5DKT and R¹× S¹ 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 S¹ in the CBEH case. We also find that in CBEH, time slices can be chosen so that a black ring with S¹× S² topology can be also formed during a certain intermediate period unlike the 5DKT.