Topology Change of Coalescing Black Holes on Eguchi-Hanson Space

TL;DR

This paper constructs five-dimensional multi-black hole solutions on Eguchi-Hanson space, demonstrating how two black holes with S^3 topology merge into a single black hole with lens space topology, and analyzing the area dependence on horizon topology.

Contribution

It introduces new multi-black hole solutions in Einstein-Maxwell theory on Eguchi-Hanson space, showing topology change during black hole coalescence.

Findings

Black holes with S^3 topology coalesce into a lens space black hole.

The horizon area after coalescence depends on the topology.

Constructed explicit solutions in five-dimensional Einstein-Maxwell theory.

Abstract

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 S^3 coalesce into a single black hole with the topology of the lens space L(2;1)=S^3/Z_2. We discuss how the area of the single black hole after the coalescence depends on the topology of the horizon.