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.
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Notes
To avoid clutter of parentheses, we will often abbreviate \(D^+(S)\) by \(D^+S\). Likewise with \(I^+\) and \(H^+\).
References
Browdy, S., Galloway, G.: Topological censorship and the topology of black holes. J. Math. Phys. 36, 4952–61 (1995)
Chruściel, P.: Geometry of Black Holes. Oxford University Press, Oxford (2020)
Chrúsciel, P., Galloway, G.: Roads to topological censorship. arXiv:1906.02151 (2019)
Chruúsciel, P., Galloway, G., Solis, D.: Topological censorship for Kaluza-Klein space-times. Annales Henri Poincare 10, 893–912 (2009)
Chrúsciel, P., Mazzeo, R.: On “many black hole’’ vacuum spacetimes. Class. Quant. Gravity 20, 729 (2003)
Friedman, J., Schleich, K., Witt, D.: Topological censorship. Phys. Rev. Lett. 71 (1993), erratum 75 (1995)
Galloway, G.: On the topology of the domain of outer communication. Class. Quant. Gravity 12, L99 (1995)
Galloway, G.: A “finite infinity’’ version of the FSW topological censorship. Class. Quant. Gravity 13, 1471 (1996)
Galloway, G., Graf, G., Ling, E.: A conformal infinity approach to asymptotically \({\text{ AdS }}_2\times S^{n-1}\) spacetimes. Annales Henri Poincaré 21, 4073–4095 (2020)
Galloway, G., Ling, E.: Topology and singularities in cosmological spacetimes obeying the null energy condition. Commun. Math. Phys. 360, 611–7 (2017)
Galloway, G., Schleich, K., Witt, D., Woolgar, E.: Topological censorship and higher genus black holes. Phys. Rev. D 60, 104039 (1999)
Galloway, G., Woolgar, E.: The cosmic censor forbids naked topology. Class. Quant. Gravity 14, L1 (1997)
Hawking, S., Ellis, G.: The Large-Scale Structure of Space-Time. Cambridge University Press, London (1973)
Hatcher, A.: Notes on Basic \(3\)-Manifold Topology
Hempel, J.: 3-Manifolds. Princeton University Press, Princeton (1976)
O’Neill, B.: Semi-Riemannian Geometry, Pure and Applied Mathematics, vol. 103. Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York (1983)
Penrose, R.: Techniques of differential topology in relativity. Society for Industrial and Applied Mathematics, Philadelphia (1972)
Planck Collaboration, Planck 2018 results, Astronomy and Astrophysics 641 (2020)
Wald, R.: General Relativity. University of Chicago Press, Chicago (1984)
Acknowledgements
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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Communicated by Mihalis Dafermos.
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Lesourd, M., Ling, E. Topological Censorship in Spacetimes Compatible with \(\Lambda > 0\). Ann. Henri Poincaré 23, 4391–4408 (2022). https://doi.org/10.1007/s00023-022-01200-1
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DOI: https://doi.org/10.1007/s00023-022-01200-1