Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-29T15:17:37.286Z Has data issue: false hasContentIssue false
  • English
  • Français

On Space-Time Singularities, Holes, and Extensions

Published online by Cambridge University Press:  01 January 2022

John Byron Manchak
Get access Rights & Permissions [Opens in a new window]

Abstract

Here, we clarify the relationship among three space-time conditions of interest: geodesic completeness, hole-freeness, and inextendibility. In addition, we introduce a related fourth condition: effective completeness.

Type
Physical Sciences
Information
Philosophy of Science , Volume 81 , Issue 5 , December 2014 , pp. 1066 - 1076
Copyright
Copyright © The Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

†

I am grateful to Erik Curiel, Bob Geroch, David Malament, and Jim Weatherall for helpful comments on previous drafts.

References

Beem, J. 1980. “Minkowski Space-Time Is Locally Extendible.” Communications in Mathematical Physics 72:273–75.CrossRefGoogle Scholar
Clarke, C. 1976. “Space-Time Singularities.” Communications in Mathematical Physics 49:17–23.CrossRefGoogle Scholar
Clarke, C. 1982. “Local Extensions in Singular Space-Times.” Communications in Mathematical Physics 84:329–31.CrossRefGoogle Scholar
Clarke, C. 1993. The Analysis of Space-Time Singularities. Cambridge: Cambridge University Press.Google Scholar
Curiel, E. 1999. “The Analysis of Singular Spacetimes.” Philosophy of Science 66 (Proceedings): S119–S145.CrossRefGoogle Scholar
Earman, J. 1989. World Enough and Space-Time. Cambridge, MA: MIT Press.Google Scholar
Earman, J. 1995. Bangs, Crunches, Whimpers, and Shrieks. Oxford: Oxford University Press.Google Scholar
Ellis, G., and Schmidt, B.. 1977. “Singular Space-Times.” General Relativity and Gravitation 8:915–53.CrossRefGoogle Scholar
Geroch, R. 1977. “Prediction in General Relativity.” In Foundations of Space-Time Theories, ed. Earman, J., Glymour, C., and Statchel, J., 81–93. Minnesota Studies in the Philosophy of Science 8. Minneapolis: University of Minnesota Press.Google Scholar
Geroch, R., Can-bin, L., and Wald, R.. 1982. “Singular Boundaries of Space-Times.” Journal of Mathematical Physics 23:432–35.CrossRefGoogle Scholar
Geroch, R., and Horowitz, G.. 1979. “Global Structure of Spacetimes.” In General Relativity: An Einstein Centenary Survey, ed. Hawking, S. and Isreal, W., 212–93. Cambridge: Cambridge University Press.Google Scholar
Hawking, S., and Ellis, G.. 1973. The Large Scale Structure of Space-Time. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Hawking, S., and Penrose, R.. 1970. “The Singularities of Gravitational Collapse and Cosmology.” Proceedings of the Royal Society A 314:529–48.Google Scholar
Krasnikov, S. 2009. “Even the Minkowski Space Is Holed.” Physical Review D 79:124041.Google Scholar
Manchak, J. 2009. “Is Spacetime Hole-Free?” General Relativity and Gravitation 41:1639–43.CrossRefGoogle Scholar
Minguzzi, E. 2012. “Causally Simple Inextendible Spacetimes Are Hole-Free.” Journal of Mathematical Physics 53:062501.CrossRefGoogle Scholar
Penrose, R. 1979. “Singularities and Time-Asymmery.” In General Relativity: An Einstein Centenary Survey, ed. Hawking, S. and Isreal, W., 581–638. Cambridge: Cambridge University Press.Google Scholar
Schmidt, B. 1971. “A New Definition of Singular Points in General Relativity.” General Relativity and Gravitation 1:269–80.CrossRefGoogle Scholar
Wald, R. 1984. General Relativity. Chicago: University of Chicago Press.CrossRefGoogle Scholar