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

Abstract

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 ${\mathrm{S}}^3$ and $L(2;1)={\mathrm{S}}^3/{\mathbb{Z}}_2$, respectively. We show that the crease sets of event horizons are topologically ${\mathrm{R}}^1$ in 5DKT and ${\mathrm{R}}^1\times {\mathrm{S}}^1$ 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 ${\mathrm{S}}^1$ in the CBEH case. We also find that in CBEH, time slices can be chosen so that a black ring with ${\mathrm{S}}^1\times {\mathrm{S}}^2$ topology can be also formed during a certain intermediate period unlike the 5DKT.

13 pages, 17 figures

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Cited by in corpus (3)

• Stability analysis of Squashed Kaluza-Klein Black Holes with Charge
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• Exact Solutions to Einstein-Maxwell theory on Eguchi-Hanson Space