Self-Similar Asymptotic Solutions of Einstein’s Equations

  • A. A. Coley
  • R. J. van den Hoogen
Part of the NATO ASI Series book series (NSSB, volume 332)


The relationship between the existence of self-similar asymptotic solutions of Einstein’s equations and equations of state is investigated. For instance, imperfect fluid Bianchi models with ‘dimensionless’ equations of state are shown to have self-similar asymptotic solutions. Conversely, it is also shown that if the spacetime is self-similar, then the resulting equations of state must be of this same ‘dimensionless’ form. The conditions under which solutions are asymptotically self-similar are discussed, and it is noted that this is not a generic property of Einstein’s equations.


Singular Point Cosmological Model Asymptotic Limit Homogeneous Function Bianchi Type 


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  1. [1]
    Wainwright, J. and Hsu L., 1989, Class. Quantum Grav., 6, 1409.MathSciNetADSMATHCrossRefGoogle Scholar
  2. [2]
    Hewitt C.G., and Wainwright J., 1993, Class. Quantum Grav., 10, 99.MathSciNetADSMATHCrossRefGoogle Scholar
  3. [3]
    Hewitt C.G. and Wainwright J., 1990, Class. Quantum Grav., 7, 2295.MathSciNetADSMATHCrossRefGoogle Scholar
  4. [4]
    Coley A.A. and van den Hoogen R.J., 1994, submitted to J. Math. Phys. Google Scholar
  5. [5]
    Ellis G.F.R. and MacCallum M.A.H., 1969, Commun. Math. Phys., 12, 108.MathSciNetADSMATHCrossRefGoogle Scholar
  6. [6]
    Hsu L. and Wainwright J., 1986, Class. Quantum Grav., 3, 1105.MathSciNetADSMATHCrossRefGoogle Scholar
  7. [7]
    MacCallum M.A.H., 1973, Cargèse Lectures in Physics, vol 6, ed E. Schatzman (New York: Gordon and Breach), p 61.Google Scholar
  8. [8]
    Coley A.A. and Tupper B.O.J., 1990, Class. Quantum Grav., 7, 1961.MathSciNetADSMATHCrossRefGoogle Scholar
  9. [9]
    Bluman G.W. and Kumei S., 1989, Symmetries and Differential Equations (New York: Springer-Verlag).MATHCrossRefGoogle Scholar
  10. [10]
    Coley A.A., 1990, J. Math. Phys., 31, 1698.MathSciNetADSMATHCrossRefGoogle Scholar
  11. [11]
    Steinhardt P.J., 1991, Proceedings of the Sixth Marcel Grossman Meeting on General Relativity, ed H. Sato and T. Nakamura (Singapore: World Scientific), p 269.Google Scholar
  12. [12]
    King A.R. and Ellis G.F.R., 1973, Commun. Math. Phys., 31, 209.MathSciNetADSMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • A. A. Coley
    • 1
  • R. J. van den Hoogen
    • 1
  1. 1.Department of Mathematics, Statistics, and Computing ScienceDalhousie UniversityHalifaxCanada

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