Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-12-05T03:04:19.214Z Has data issue: false hasContentIssue false
  • English
  • Français

What Is a Singularity in Geometrized Newtonian Gravitation?

Published online by Cambridge University Press:  01 January 2022

James Owen Weatherall
Get access Rights & Permissions [Opens in a new window]

Abstract

I discuss singular space-times in the context of the geometrized formulation of Newtonian gravitation. I argue first that geodesic incompleteness is a natural criterion for when a model of geometrized Newtonian gravitation is singular, and then I show that singularities in this sense arise naturally in classical physics by stating and proving a classical version of the Raychaudhuri-Komar singularity theorem.

Type
Physical Sciences
Information
Philosophy of Science , Volume 81 , Issue 5 , December 2014 , pp. 1077 - 1089
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

†

Thank you to my fellow symposiasts, Erik Curiel and John Manchak; to Jeremy Butterfield, who chaired the session; and to the audience at the PSA 2012 biennial meeting for their helpful comments and questions. I am especially indebted to David Malament for helpful discussions and for detailed comments on a previous draft.

References

Cartan, E. 1923. “Sur les variétés à connexion affine, et la théorie de la relativité généralisée.” Pt. 1. Annales scientifiques de l’École Normale Supérieure 40:325–412.10.24033/asens.751CrossRefGoogle Scholar
Cartan, E. 1924. “Sur les variétés à connexion affine, et la théorie de la relativité généralisée.” Pt. 2. Annales scientifiques de l’École Normale Supérieure 41:1–25.10.24033/asens.753CrossRefGoogle Scholar
Choquet-Bruhat, Y. 2009. General Relativity and the Einstein Equations. New York: Oxford University Press.Google Scholar
Clarke, C. J. S. 1993. The Analysis of Space-Time Singularities. New York: Cambridge University Press.Google Scholar
Curiel, E. 1999. “The Analysis of Singular Spacetimes.” Philosophy of Science 66:S119–S145.CrossRefGoogle Scholar
Earman, J. 1995. Bangs, Crunches, Whimpers, and Shrieks. New York: Oxford University Press.Google Scholar
Earman, J. 1999. “The Penrose-Hawking Singularity Theorems: History and Implications.” In The Expanding Worlds of General Relativity, ed. Goenner, H., Renn, J., Ritter, J., and Sauer, T., 235–67. Boston: Birkhäuser.Google Scholar
Ellis, G. F. R., and Schmidt, B. G.. 1977. “Singular Space-Times.” General Relativity and Gravitation 8 (11): 915–53.10.1007/BF00759240CrossRefGoogle Scholar
Friedrichs, K. O. 1927. “Eine invariante formulierun des newtonschen gravitationsgesetzes und der grenzüberganges vom einsteinschen zum newtonschen gesetz.” Mathematische Annalen 98:566–75.Google Scholar
Geroch, R. 1968. “What Is a Singularity in General Relativity?” Annals of Physics 48 (3): 526–40.10.1016/0003-4916(68)90144-9CrossRefGoogle Scholar
Geroch, R. 1970. “Singularities.” In Relativity, 259–91. New York: Plenum.Google Scholar
Glymour, C. 1970. “Theoretical Equivalence and Theoretical Realism.” In PSA 1970: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 275–88. East Lansing, MI: Philosophy of Science Association.Google Scholar
Hawking, S. W., and Ellis, G. F. R.. 1973. The Large Scale Structure of Space-Time. New York: Cambridge University Press.CrossRefGoogle Scholar
Heckmann, O., and Schücking, E.. 1955. “Bemerkungen zur Newtonschen Kosmologie.” Zeitschrift für Astrophysik 38:95–109.Google Scholar
Knox, E. 2013. “Newtonian Spacetime Structure in Light of the Equivalence Principle.” British Journal for Philosophy of Science, forthcoming.Google Scholar
Komar, A. 1956. “Necessity of Singularities in the Solution of the Field Equations of General Relativity.” Physical Review 104 (2): 544–46.10.1103/PhysRev.104.544CrossRefGoogle Scholar
Malament, D. B. 2012. Topics in the Foundations of General Relativity and Newtonian Gravitation Theory. Chicago: University of Chicago Press.10.7208/chicago/9780226502472.001.0001CrossRefGoogle Scholar
Raychaudhuri, A. 1955. “Relativistic Cosmology.” Pt. 1. Physical Review 98 (4): 1123–26.CrossRefGoogle Scholar
Ruede, C., and Straumann, N.. 1997. “On Newton-Cartan Cosmology.” Helvetica Physica Acta 70:318–35.Google Scholar
Sachs, R. K., and Wu, H.. 1977. General Relativity for Mathematicians. New York: Springer.CrossRefGoogle Scholar
Senovilla, J. M. M. 1997. “Singularity Theorems and Their Consequences.” General Relativity and Gravitation 29 (5): 701–848.Google Scholar
Senovilla, J. M. M., Sopuerta, C. F., and Szekeres, P.. 1998. “Theorems on Shear-Free Perfect Fluids with Their Newtonian Analogues.” General Relativity and Gravitation 30 (3): 389–411.CrossRefGoogle Scholar
Tipler, F., Clarke, C. J. S., and Ellis, G. F. R.. 1980. “Singularities and Horizons—a Review Article.” In General Relativity and Gravitation, Vol. 2, ed. A. Held, 97–206. New York: Plenum.Google Scholar
Trautman, A. 1965. “Foundations and Current Problem of General Relativity.” In Lectures on General Relativity, ed. Deser, S. and Ford, K. W., 1–248. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
Wald, R. M. 1984. General Relativity. Chicago: University of Chicago Press.10.7208/chicago/9780226870373.001.0001CrossRefGoogle Scholar
Weatherall, J. O. 2013. “Gauge Transformations, Theoretical Equivalence, and the Interpretation of Physical Theories.” Unpublished manuscript, University of California, Irvine.Google Scholar