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Interpreting Non-Hausdorff (Generalized) Manifolds in General Relativity

Published online by Cambridge University Press:  01 January 2022

Joanna Luc  and
Tomasz Placek
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Abstract

The article investigates the relations between Hausdorff and non-Hausdorff manifolds as objects of general relativity. We show that every non-Hausdorff manifold can be seen as a result of gluing together some Hausdorff manifolds. In the light of this result, we investigate a modal interpretation of a non-Hausdorff differential manifold, according to which it represents a bundle of alternative space-times, all of which are compatible with a given initial data set.

Type
Articles
Information
Philosophy of Science , Volume 87 , Issue 1 , January 2020 , pp. 21 - 42
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

We gratefully acknowledge the support of the National Science Center for Joanna Luc (research grant Opus 2016/23/B/HS1/00464 ) and the support of the WSN2017 program of the Foundation for Polish Science for Tomasz Placek. For fruitful discussions we thank the audiences of meetings of the Southern California Philosophy of Physics Group, British Society for the Philosophy of Science Annual Conference in Oxford, and Modality in Physics conference in Kraków. We are also grateful to three anonymous referees of this journal for their helpful comments.

References

Belnap, N. 1992. “Branching Space-Time.” Synthese 92:385–434.CrossRefGoogle Scholar
Belot, G. 1995. “New Work for Counterpart Theorists: Determinism.” British Journal for the Philosophy of Science 46:185–95.CrossRefGoogle Scholar
Bressan, A. 1980. “On Physical Possibility.” In Italian Studies in the Philosophy of Science, ed. Dalla Chiara, M. L., 197–210. Dordrecht: Reidel.CrossRefGoogle Scholar
Choquet-Bruhat, Y., and Geroch, R. 1969. “Global Aspects of the Cauchy Problem in General Relativity.” Communications in Mathematical Physics 14:329–35.CrossRefGoogle Scholar
Chruściel, P. 1991. On Uniqueness in the Large of Solutions of Einstein’s Equations (Strong Cosmic Censorship). Proceedings of the Centre for Mathematics and its Applications 27. Canberra: Australian National University.Google Scholar
Chruściel, P. 2011. “Elements of Causality Theory.” arXiv, Cornell University. https://arxiv.org/abs/1110.6706.Google Scholar
Chruściel, P. T., and Isenberg, J. 1993. “Nonisometric Vacuum Extensions of Vacuum Maximal Globally Hyperbolic Spacetimes.” Physical Review D 48 (4): 1616–28.CrossRefGoogle ScholarPubMed
Divers, J. 2002. Possible Worlds. London: Routledge.Google Scholar
Earman, J. 2008. “Pruning Some Branches from Branching Spacetimes.” In The Ontology of Spacetime II, ed. Dieks, D., 187–206. Amsterdam: Elsevier.CrossRefGoogle Scholar
Geroch, R. 1968. “Local Characterization of Singularities in General Relativity.” Journal of Mathematical Physics 9:450–65.CrossRefGoogle Scholar
Hájíček, P. 1971a. “Bifurcate Space-Times.” Journal of Mathematical Physics 12 (1): 157–60.CrossRefGoogle Scholar
Hájíček, P. 1971b. “Causality in Non-Hausdorff Space-Times.” Communications in Mathematical Physics 21:75–84.CrossRefGoogle Scholar
Hawking, S. W., and Ellis, G. F. R. 1973. The Large Scale Structure of Space-Time. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Kervaire, M. A. 1960. “A Manifold Which Does Not Admit Any Differentiable Structure.” Commentarii Mathematici Helvetici 34 (1): 257–70.CrossRefGoogle Scholar
Luc, J. 2019. “Generalised Manifolds as Basic Objects of General Relativity.” Foundations of Physics, forthcoming.CrossRefGoogle Scholar
Margalef-Bentabol, J., and Villaseñor, E. J. S. 2014. “Topology of the Misner Space and Its g-Boundary.” General Relativity and Gravitation 46 (7): 1755.CrossRefGoogle Scholar
Melia, J. 1999. “Holes, Haecceitism and Two Conceptions of Determinism.” British Journal for the Philosophy of Science 50 (4): 639–64.CrossRefGoogle Scholar
Newman, E., Tamburino, L., and Unti, T. 1963. “Empty-Space Generalization of the Schwarzschild Metric.” Journal of Mathematical Physics 4:915–25.CrossRefGoogle Scholar
Penrose, R. 1979. “Singularities and Time-Asymmetry.” In General Relativity: An Einstein Centenary Survey, ed. Hawking, S. and Israel, W., 581–638. Cambridge: Cambridge University Press.Google Scholar
Sattig, T. 2015. “Pluralism and Determinism.” Journal of Philosophy 111:135–50.Google Scholar