On "many black hole" space-times

TL;DR

This paper investigates the horizon structure of multi-black hole space-times, demonstrating under certain conditions that the outermost apparent horizons and event horizons can have multiple disconnected components, confirming their 'many black hole' nature.

Contribution

It provides a rigorous analysis showing that under smallness conditions, multi-black hole initial data lead to space-times with multiple disconnected horizons, supporting the 'many black holes' concept.

Findings

Outer apparent horizons can have multiple components.

Event horizons in these space-times are disconnected.

Supports the 'many black hole' characterization of certain solutions.

Abstract

We analyze the horizon structure of families of space times obtained by evolving initial data sets containing apparent horizons with several connected components. We show that under certain smallness conditions the outermost apparent horizons will also have several connected components. We further show that, again under a smallness condition, the maximal globally hyperbolic development of the many black hole initial data constructed by Chrusciel and Delay, or of hyperboloidal data of Isenberg, Mazzeo and Pollack, will have an event horizon, the intersection of which with the initial data hypersurface is not connected. This justifies the "many black hole" character of those space-times.