Topology Change of Coalescing Black Holes on Eguchi-Hanson Space

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We construct multi-black hole solutions in the five-dimensional Einstein-Maxwell theory with a positive cosmological constant on the Eguchi-Hanson space, which is an asymptotically locally Euclidean space. The solutions describe the physical process such that two black holes with the topology of S³ coalesce into a single black hole with the topology of the lens space L(2;1)=S³/Z₂. We discuss how the area of the single black hole after the coalescence depends on the topology of the horizon.