Hostname: page-component-745bb68f8f-b95js Total loading time: 0 Render date: 2025-01-15T18:55:55.128Z Has data issue: false hasContentIssue false
  • English
  • Français

Global properties of locally spatially homogeneous cosmological models with matter

Published online by Cambridge University Press:  24 October 2008

Alan D. Rendall
Alan D. Rendall
Affiliation:
Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, Postfach 1523, 85740 Garching, Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

The existence and nature of singularities in locally spatially homogeneous solutions of the Einstein equations coupled to various phenoraenological matter models is investigated. It is shown that, under certain reasonable assumptions on the matter, there are no singularities in an expanding phase of the evolution and that unless the spacetime is empty a contracting phase always ends in a singularity where at least one scalar invariant of the curvature diverges uniformly. The class of matter models treated includes perfect fluids, mixtures of non-interacting perfect fluids and collisionless matter.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 118 , Issue 3 , November 1995 , pp. 511 - 526
Copyright
Copyright © Cambridge Philosophical Society 1995

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.)

References

REFERENCES

[1]Burnett, G.. Incompleteness theorems for the spherically symmetric spacetimes. Phys. Rev. D43 (1991), 1143–1149.Google Scholar
[2]Cercignani, C.. The Boltzmann equation and its applications (Springer, 1988).CrossRefGoogle Scholar
[3]Chruściel, P. T. and Rendall, A. D.. Preprint gr-qc/9410040 (1994).Google Scholar
[4]Coley, A. A. and Wainwright, J.. Qualitative analysis of two-fluid Bianchi cosmologies. Class. Quantum Grav. 9 (1992), 651–665.CrossRefGoogle Scholar
[5]Collins, C. B.. Global structure of the Kantowski-Sachs cosmological models. J. Math. Phys. 18 (1977), 2116–2124.CrossRefGoogle Scholar
[6]Collins, C. B. and Ellis, G. F. R.. Singularities in Bianchi cosmologies. Physics Reports 56 (1979), 65–105.CrossRefGoogle Scholar
[7]Ehlers, J.. Survey of general relativity. In Relativity, astrophysics and cosmology. (Reidel, 1973).Google Scholar
[8]Glassey, R. and Strauss, W.. Asymptotic stability of the relativistic Maxwellian. Publ. R.I.M.S. Kyoto Univ. 29 (1993), 301–347.CrossRefGoogle Scholar
[9]Hartman, P.. Ordinary differential equations. 2nd Ed. (Birkhäuser, 1982).Google Scholar
[10]Hawking, S. W. and Ellis, G. F. B.. The large scale structure of space-time. (Cambridge University Press, 1973).CrossRefGoogle Scholar
[11]Lin, X.-F. and Wald, R.. Proof of the closed universe recollapse conjecture for general Bianchi type IX cosmologies. Phys. Rev. D41 (1990), 2444–2448.Google Scholar
[12]Rendall, A. D.. Cosmic censorship for some spatially homogeneous cosmological models. Ann. Phys. 233 (1994), 82–96.CrossRefGoogle Scholar
[13]Rendall, A. D.. On the nature of singularities in plane symmetric scalar field cosmologies. Preprint gr-qc/9408001 (1994).Google Scholar
[14]Singer, I. M.. Infinitesimally homogeneous spaces. Commun. Pure Appl. Math. 13 (1960), 685–697.CrossRefGoogle Scholar
[15]Wald, R.. Asymptotic behaviour of homogeneous cosmological models in the presence of a positive cosmological constant. Phys. Rev. D28 (1983), 2118–2120.Google Scholar
[16]Wald, R.. General Relativity. (University of Chicago Press, 1984).CrossRefGoogle Scholar