Topological censorship in spacetimes compatible with $\Lambda > 0$

TL;DR

This paper extends topological censorship theorems to universes with positive cosmological constant, showing that black hole regions become topologically simple over time despite complex overall universe topology.

Contribution

It proves a new topological censorship theorem applicable to $ ext{Lambda}>0$ universes, allowing for multiple black hole collections and late-time isolation.

Findings

Black hole regions have trivial fundamental group at late times.

The theorem applies to universes with multiple black hole collections.

Nontrivial global topology can exist despite local topological simplicity.

Abstract

Currently available topological censorship theorems are meant for gravitationally isolated black hole spacetimes with cosmological constant $\Lambda=0$ or $\Lambda<0$. Here, we prove a topological censorship theorem that is compatible with $\Lambda>0$ and which can be applied to whole universes containing possibly multiple collections of black holes. The main assumption in the theorem is that distinct black hole collections eventually become isolated from one another at late times, and the conclusion is that the regions near the various black hole collections have trivial fundamental group, in spite of there possibly being nontrivial topology in the universe.