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Topological Censorship in Spacetimes Compatible with \(\Lambda > 0\)


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.

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  1. To avoid clutter of parentheses, we will often abbreviate \(D^+(S)\) by \(D^+S\). Likewise with \(I^+\) and \(H^+\).


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Martin Lesourd thanks the John Templeton and Gordon Betty Moore foundations for their support of the Black Hole Initiative. Eric Ling thanks the Harold H. Martin Postdoctoral Fellowship. Finally, both authors would like to express their thanks to Greg Galloway, with whom we discussed examples which greatly improved our understanding.

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Correspondence to Martin Lesourd.

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Communicated by Mihalis Dafermos.

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Lesourd, M., Ling, E. Topological Censorship in Spacetimes Compatible with \(\Lambda > 0\). Ann. Henri Poincaré (2022).

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