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On the topology of black holes

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Abstract

We establish from local hypotheses some results concerning the final state topology of black holes. We show that the surface of a black hole must have 2-sphere topology and that the topology of space in its vicinity is simple.

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References

  • [BM] Bunting, G.L., Masood-ul-Alam, A.K.M.: Nonexistence of multiple black holes in asymptotically euclidean static vacuum space-times Gen. Rel. Grav. J.19, 147–154 (1987)

    Google Scholar 

  • [FG] Frankel, T., Galloway, G.J.: Stable minimal surfaces and spatial topology in general relativity. Math. Zeit.181, 396–406 (1982)

    Google Scholar 

  • [E] Eschenburg, J.-H.: Maximum principle for hypersurfaces. Manuscripta Math.64, 55–75 (1989)

    Google Scholar 

  • [G] Gannon, D.: Singularities in nonsimply connected space-times. J. Math. Phys.16, 2364–2367 (1975)

    Google Scholar 

  • [HE] Hawking, S.W., Ellis, G.F.R.: The large scale structure of space-time. Cambridge: Cambridge University Press 1973

    Google Scholar 

  • [L] Lee, C.W.: A restriction on the topology of Cauchy surfaces in general relativity. Commun. Math. Phys.51, 157–162 (1976)

    Google Scholar 

  • [M-A] Masood-ul-Alam, A.K.M.: The topology of asymptotically euclidean static perfect fluid space-time. Commun. Math. Phys.108, 193–211 (1987)

    Google Scholar 

  • [MSY] Meeks, W., Simon, L., Yau, S.-T.: Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature. Ann. Math.116, 621–659 (1982)

    Google Scholar 

  • [MTY] Morris, M.S., Thorne, K.S., Yurtsever, U.: Wormholes, time machines, and the weak energy condition. Phys. Rev. Lett.61, 1446–1449 (1988)

    Google Scholar 

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Communicated by S.-T. Yau

Dedicated to Ted Frankel

This work has been partially supported by NSF grants DMS-8802877 and DMS-9006678

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Galloway, G.J. On the topology of black holes. Commun.Math. Phys. 151, 53–66 (1993). https://doi.org/10.1007/BF02096748

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  • DOI: https://doi.org/10.1007/BF02096748

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