Abstract
Here, we examine hole-freeness—a condition sometimes imposed to rule out seemingly artificial spacetimes. We show that under existing definitions (and contrary to claims made in the literature) there exist inextendible, globally hyperbolic spacetimes which fail to be hole-free. We then propose an updated formulation of the condition which enables us to show the intended result. We conclude with a few general remarks on the strength of the definition and then formulate a precise question which may be interpreted as: Are all physically reasonable spacetimes hole-free?
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References
Clarke C.J.S.: Space-time singularities. Commun. Math. Phys. 49, 17–23 (1976)
Clarke C.J.S.: Singularities: global and local Aspects. In: Bergmann, P.G., De Sabbata, V. (eds) Topological Properties and Global Structure of Space-Time, pp. 61–72. Plenum Press, New York (1986)
Clarke C.J.S.: The Analysis of Space-Time Singularities. Cambridge University Press, Cambridge (1993)
Clarke C.J.S., Schmidt B.: Singularities: The State of the Art. Gen. Relativ. Gravit. 8, 129–137 (1977)
Earman J.: A Primer on Determinism. D. Reidel, Dordrecht (1986)
Earman J.: Bangs, Crunches, Whimpers, and Shrieks. Oxford University Press, Oxford (1995)
Ellis G.F.R., Schmidt B.: Singular space-times. Gen Relativ Gravit 8, 915–953 (1977)
Geroch R.: Prediction in general relativity. In: Earman, J., Glymour, C., Statchel, J.(eds) Foundations of Space-Time Theories, Minnesota Studies in the Philosophy of Science, vol. VIII, pp. 81–93. University of Minnesota Press, Minneapolis (1977)
Geroch R., Horowitz G.: Global Structure of Spacetimes. In: Hawking, S., Isreal, W.(eds) General Relativity: An Einstein Centenary Survey, pp. 212–293. Cambridge University Press, Cambridge (1979)
Hawking S., Ellis G.F.R.: The Large Scale Structure of Space-Time. Cambridge University Press, Cambridge (1973)
Steinmüller B., King A., Lasota J.: Radiating bodies and naked singularites. Phys. Lett. A 51, 191 (1975)
Wald R.: General Relativity. University of Chicago Press, Chicago (1984)
Acknowledgments
I wish to thank John Earman and Robert Geroch for helpful discussions on this topic.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Manchak, J.B. Is spacetime hole-free?. Gen Relativ Gravit 41, 1639–1643 (2009). https://doi.org/10.1007/s10714-008-0734-1
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DOI: https://doi.org/10.1007/s10714-008-0734-1