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Topology of Event Horizons and Topological Censorship | | Ted Jacobson
; Shankar Venkataramani
; | | Date: |
18 Oct 1994 | | Journal: | Class.Quant.Grav. 12 (1995) 1055-1062 | | Subject: | gr-qc hep-th | | 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 $C_K$ to the future of a cut $K$ of $Sm$ is globally hyperbolic. Suppose further that a Cauchy surface $Sigma$ for $C_K$ is a topological 3-manifold with compact boundary $partialS$ in $M$, and $S’$ is a compact submanifold of $S$ with spherical boundary in $S$ (and possibly other boundary components in $M/S$). Then we prove that the homology group $H_1(Sigma’,Z)$ must be finite. This implies that either $partialS’$ consists of a disjoint union of 2-spheres, or $S’$ is nonorientable and $partialS’$ contains a projective plane. Further, $partialS=partialIp[K]cappartialIm[Sp]$, and $partial Sigma$ will be a cross section of the horizon as long as no generator of $partialIp[K]$ becomes a generator of $partialIm[Sp]$. In this case, if $S$ is orientable, the horizon cross section must consist of a disjoint union of 2-spheres.} | | Source: | arXiv, gr-qc/9410023 | | Services: | Forum | Review | PDF | Favorites | |
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