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## Banach Center Publications

1997 | 41 | 1 | 233-242
Tytuł artykułu

### Fastest curves and toroidal black holes

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EN
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EN
We discuss an apparent paradox (and conjectured resolution) of Jacobson and Venkataramani concerning 'temporarily toroidal' black hole horizons, in light of a recent connectivity theorem for spaces of complete causal curves. We do this in a self-contained manner by first reviewing the 'fastest curve argument' which proves this connectivity theorem, and we note that active topological censorship can be derived as a corollary of this argument. We argue that the apparent paradox arises only when one dispenses with the invariant viewpoint provided by the connectivity theorem in favour of an observer-dependent description. Finally, we discuss an alternative to fastest curve arguments, which can be used to construct a self-contradictory null line in certain spacetimes violating topological censorship. These arguments may shed light on the relationship between topological and cosmic censorship.
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233-242
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wydano
1997
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Bibliografia
• [1] A. Borde, Geodesic focusing, energy conditions and singularities, Class. Quantum Gravit. 4 (1987), 343-356.
• [2] P. T. Chruściel and R. M. Wald, On the topology of stationary black holes, Class. Quantum Gravit. 11 (1994), L147-L152.
• [3] J. L. Friedman, K. Schleich, and D. W. Witt, Topological censorship, Phys. Rev. Lett. 71 (1993), 1486-1489.
• [4] G. Galloway, On the topology of the domain of outer communication, Class. Quantum Gravit. 12 (1995), L99-L101.
• [5] D. Gannon, Singularities in nonsimply connected space-times, J. Math. Phys. 16 (1975), 2364-2367.
• [6] S. A. Hughes, et al., Finding Black Holes in Numerical Spacetimes, Phys. Rev. D49 (1994), 4004-4015.
• [7] T. Jacobson and S. Venkataramani, Topology of event horizons and topological censorship, Class. Quantum Gravit. 12 (1995), 1055-1061.
• [8] R. Penrose, R. D. Sorkin, and E. Woolgar, A positive mass theorem based on the focusing and retardation of null geodesics, preprint gr-qc/9301015, 1993; R. Penrose Light rays near $i^0$: a new mass-positivity theorem, Twistor Newsletter 30 (1990), 1-5; R. D. Sorkin and E. Woolgar, New demonstration of the positivity of mass, in: Proc. Fourth Can. Conf. on Gen. Rel. and Rel. Astrophys. , G. Kunstatter, D. E. Vincent, and J. G. Williams (eds.), World Scientific, Singapore, 1992, 206-210.
• [9] R. Penrose, R. D. Sorkin, and E. Woolgar, in preparation.
• [10] I. I. Shapiro, Fourth test of general relativity, Phys. Rev. Lett. 13 (1964), 789-791.
• [11] R. D. Sorkin and E. Woolgar, A causal order for spacetimes with $C^0$ Lorentzian metrics: proof of compactness of the space of causal curves, Class. Quantum Gravit., to appear (1996) (cf. gr-qc/9508018).
• [12] F. J. Tipler, Energy conditions and spacetime singularities, Phys. Rev. D17 (1978), 2521-2528; T. A. Roman, Quantum stress-energy tensors and the weak energy condition, Phys. Rev. D33 (1986), 3526-3533; On the 'averaged weak energy condition' and Penrose's singularity theorem, Phys. Rev. D 37 (1988), 546-548.
• [13] G. J. Galloway and E. Woolgar, The cosmic censor forbids naked topology, Class. Quantum Gravit. 14 (1997), L1-L7.
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Bibliografia
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