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Letters in Mathematical Physics

, Volume 109, Issue 3, pp 661–673 | Cite as

New restrictions on the topology of extreme black holes

  • Marcus Khuri
  • Eric WoolgarEmail author
  • William Wylie
Article

Abstract

We provide bounds on the first Betti number and structure results for the fundamental group of horizon cross sections for extreme stationary vacuum black holes in arbitrary dimension, without additional symmetry hypotheses. This is achieved by exploiting a correspondence between the associated near-horizon geometries and the mathematical notion of m-quasi-Einstein metrics, in addition to generalizations of the classical splitting theorem from Riemannian geometry. Consequences are analyzed and refined classifications are given for the possible topologies of these black holes.

Keywords

Black holes Horizon topology m-Quasi-Einstein metric Splitting theorem 

Mathematics Subject Classification

83C57 53C20 

Notes

Acknowledgements

The authors would like to thank Hari Kunduri for comments, as well as Stefan Hollands and James Lucietti for independently pointing out that \(\mathbb {RP}^3 \#\mathbb {RP}^3\) can be ruled out in Corollary 7 when an extra U(1) symmetry is present. The first author would also like to thank Luca Di Cerbo for useful discussions.

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of MathematicsStony Brook UniversityStony BrookUSA
  2. 2.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada
  3. 3.Department of MathematicsSyracuse UniversitySyracuseUSA

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