Topological Censorship in Spacetimes Compatible with $$\Lambda > 0$$

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.