Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-26T03:08:08.798Z Has data issue: false hasContentIssue false
  • English
  • Français

The Analysis of Singular Spacetimes

Published online by Cambridge University Press:  01 April 2022

Erik Curiel
Erik Curiel*
Affiliation:
Stanford University
*
†Philosophy Department, Stanford University, Palo Alto, CA 94305–2155; e-mail: encuriel@csli.stanford.edu.
Get access Rights & Permissions [Opens in a new window]

Abstract

Much controversy surrounds the question of what ought to be the proper definition of ‘singularity’ in general relativity, and the question of whether the prediction of such entities leads to a crisis for the theory. I argue that a definition in terms of curve incompleteness is adequate, and in particular that the idea that singularities correspond to ‘missing points’ has insurmountable problems. I conclude that singularities per se pose no serious problem for the theory, but their analysis does bring into focus several problems of interpretation at the foundation of the theory often ignored in the philosophical literature.

Type
Foundations of Statistical Physics, Spacetime Theories, and Quantum Field Theory
Information
Philosophy of Science , Volume 66 , Issue S3: Supplement. Proceedings of the 1998 Biennial Meetings of the Philosophy of Science Association. Part I: Contributed Papers Sep., 1999 , 1999 , pp. S119 - S145
Copyright
Copyright © 1999 by 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

‡

This paper began life as a small criticism of a few points John Earman makes in Chapter 2 of his book Bangs, Crunches, Whimpers and Shrieks, and grew as I grew to realize more fully the complexity and subtlety of the issues involved. I shall not always point out where I am in agreement or disagreement with Earman, much less always discuss why this is so, though I shall try to on the most important points. The reader ought to keep in mind, though, that Earman's book is the constant foil lurking in the background. I thank R. Geroch and D. Malament for stimulating conversations on all these topics. I am also grateful to M. Dorato for writing a review of Earman 1995 that made me realize the need to reread it and think more about singular structure, and to the History and Philosophy of Science Department at Pittsburgh, where I presented an earlier, briefer, version of this paper in a colloquium, for stimulating questions.

References

Belot, G. (1996), “Why General Relativity Does Need an Interpretation”, Philosophy of Science 63 (Proceedings): S80–S88.CrossRefGoogle Scholar
Bosshard, B. (1976), “On the b-boundary of the closed Friedmann model,” Communications in Mathematical Physics 46: 263–268.CrossRefGoogle Scholar
Clarke, C. (1973), “Local Extensions in Singular Space-Times”, Communications in Mathematical Physics 32: 205–214.CrossRefGoogle Scholar
Clarke, C. (1975), “Singularities in Globally Hyperbolic Space-Times”, Communications in Mathematical Physics 41: 65–78.CrossRefGoogle Scholar
Clarke, C. (1993), The Analysis of Space-Time Singularities. Number 1 in Cambridge Lecture Notes in Physics. Cambridge: Cambridge University Press.Google Scholar
Curiel, E. (1998), “Is Energy a Well-Defined Quantity in the Theory of General Relativity?” (unpublished).Google Scholar
Earman, J. (1995), Bangs, Crunches, Whimpers and Shrieks: Singularities and Acausalities in Relativistic Spacetimes. Oxford: Oxford University Press.Google Scholar
Ellis, G. and Schmidt, B. (1977), “Singular Space-times.” General Relativity and Gravitation 8: 915–953.CrossRefGoogle Scholar
Geroch, R. (1966), “Singularities in Closed Universes,” Physical Review Letters 17: 445–447.CrossRefGoogle Scholar
Geroch, R. (1968a), “Local Characterization of Singularities in General Relativity”, Journal of Mathematical Physics 9: 450–465.10.1063/1.1664599CrossRefGoogle Scholar
Geroch, R. (1968b), “What is a Singularity in General Relativity?”, Annals of Physics 48: 526–540.CrossRefGoogle Scholar
Geroch, R. (1985), Mathematical Physics. Chicago: University of Chicago Press.Google Scholar
Geroch, R., Can-bin, L., and Wald, R. (1982), “Singular Boundaries of Space-Times”, Journal of Mathematical Physics 23: 432–435.CrossRefGoogle Scholar
Geroch, R., Kronheimer, E., and Penrose, R. (1972) “Ideal Points in Space-Time”, Philosophical Transactions of the Royal Society (London) A327: 545–567.Google Scholar
Hawking, S. (1965), “Occurrence of Singularities in Open Universes,” Physical Review Letters 15: 689–690.CrossRefGoogle Scholar
Hawking, S. (1967), “The Occurrence of Singularities in Cosmology, III”, Philosophical Transactions of the Royal Society (London) A300: 187–210.Google Scholar
Hawking, S. and Ellis, G. (1973), The Large Scale Structure of Space-Time. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Hocking, J. and Young, G. (1988), Topology. New York: Dover Publications, Inc. Originally published in 1961 by Addison-Wesley Publishing Co.Google Scholar
Johnson, R. (1977), “The Bundle Boundary in Some Special Cases”, Journal of Mathematical Physics 18: 898–902.CrossRefGoogle Scholar
Joshi, P. (1993), Global Aspects in Gravitation and Cosmology. Number 87 in International Series of Monographs on Physics. Oxford: Oxford University Press.Google Scholar
Konkowski, D. and Helliwell, T. (1992), “Singularities in Colliding Plane-Wave Spacetimes”, in Kunstatter, G. (ed.), General Relativity and Relativistic Astrophysics. Singapore: World Scientific Publishing Co., 115–119.Google Scholar
Kuchaf, K. (1992), “Time and Interpretations of Quantum Gravity”, in Kunstatter, G. et al. (eds.), General Relativity and Relativistic Astrophysics. Singapore: World Scientific Publishing Co., 211–314.Google Scholar
Misner, C. (1963), “The Flatter Regions of Newman, Unti, and Tamburino's Generalized Schwarzschild Space”, Journal of Mathematical Physics 4: 924–937.CrossRefGoogle Scholar
Misner, C., Thorne, K., and Wheeler, J. (1973), Gravitation. San Francisco: Freeman Press.Google Scholar
Penrose, R. (1960), “A Spinor Approach to General Relativity.” Annals of Physics 10: 171–201.CrossRefGoogle Scholar
Penrose, R. (1965), “Gravitational Collapse and Space-Time Singularities”, Physical Review Letters 14: 57–59.10.1103/PhysRevLett.14.57CrossRefGoogle Scholar
Schmidt, B. (1971), “A New Definition of Singular Points in General Relativity”, General Relativity and Gravitation 1: 269–280.CrossRefGoogle Scholar
Scott, S. and Szekeres, P. (1994), “The Abstract Boundary—a New Approach to Singularities of Manifolds”, Journal of Geometry and Physics 13: 223–253.CrossRefGoogle Scholar
Shepley, L. and Ryan, G. (1978), Homogeneous Cosmological Models. Princeton: Princeton University Press.Google Scholar
Spivak, M. (1979). A Comprehensive Introduction to Differential Geometry, 2nd ed. vol. 1. Houston: Publish or Perish Press. First edition published in 1970.Google Scholar
Stein, H. (1984), “The Everett Interpretation of Quantum Mechanics: Many Worlds or None?”, Noûs 18: 635–652.CrossRefGoogle Scholar
Sussmann, R. (1988), “On Spherically Symmetric Shear-Free Perfect Fluid Configurations (Neutral and Charged), II. Equation of State and Singularities”, Journal of Mathematical Physics 29:945–970.10.1063/1.527992CrossRefGoogle Scholar
Taub, A. (1979), “Remarks on the Symposium on Singularities”, General Relativity and Gravitation 10: 1009.CrossRefGoogle Scholar
Thorpe, J. (1977), “Curvature Invariants and Space-Time Singularities”, Journal of Mathematical Physics 18: 960–964.CrossRefGoogle Scholar
Wald, R. (1984), General Relativity. University of Chicago Press.10.7208/chicago/9780226870373.001.0001CrossRefGoogle Scholar