Topology of event horizons and topological censorship

Ted Jacobson, Shankar Venkataramani

Research output: Contribution to journalArticle

73 Scopus citations

Abstract

We prove that, under certain conditions, the topology of the event horizon of a four-dimensional asymptotically flat black-hole spacetime must be a 2-sphere. No stationarity assumption is made. However, in order for the theorem to apply, the horizon topology must be unchanging for long enough to admit a certain kind of cross section. We expect this condition is generically satisfied if the topology is unchanging for much longer than the light-crossing time of the black hole. More precisely, let M be a four-dimensional asymptotically flat spacetime satisfying the averaged null energy condition, and suppose that the domain of outer communication to the future of a cut K of is globally hyperbolic. Suppose further that a Cauchy surface for is a topological 3-manifold with compact boundary in M, and is a compact submanifold of with spherical boundary in (and possibly other boundary components in ). Then we prove that the homology group must be finite. This implies that either consists of a disjoint union of 2-spheres, or is non-orientable and contains a projective plane. Furthermore, , and will be a cross section of the horizon as long as no generator of becomes a generator of . In this case, if is orientable, the horizon cross section must consist of a disjoint union of 2-spheres.

Original languageEnglish (US)
Article number012
Pages (from-to)1055-1061
Number of pages7
JournalClassical and Quantum Gravity
Volume12
Issue number4
DOIs
StatePublished - 1995

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

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