On the Dynamics of Generators of Cauchy Horizons

  • P. T. Chruściel
  • J. Isenberg
Part of the NATO ASI Series book series (NSSB, volume 332)


We discuss various features of the dynamical system determined by the flow of null geodesic generators of Cauchy horizons. Several examples with non-trivial global behaviour are constructed.


Vector Field Periodic Orbit Cauchy Horizon Lorenz Attractor Closed Timelike Curve 
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  1. [1]
    Hawking, S.W., 1992, “Chronology protection conjecture”, Phys. Rev., D46, 603–611.MathSciNetADSGoogle Scholar
  2. [2]
    Thorne, K.S., 1993, “Closed time-like curves”, in General Relativity and Gravitation 13, R.J. Gleiser, C.N. Kozameh, O.M. Moreschi, eds., (Bristol: Institute of Physics).Google Scholar
  3. [3]
    Visser, M., 1993, “Van Vleck determinants: traversable wormhole spacetimes”, preprint, gr-qc/9311026.Google Scholar
  4. [4]
    Hawking, S.W., Ellis, G.F.R., 1973, The Large Scale Structure of Space-time, (Cambridge: Cambridge University Press).zbMATHCrossRefGoogle Scholar
  5. [5]
    Smale, S., 1967, “Differential dynamical systems”, Bull AMS, 73, 747–817.MathSciNetzbMATHCrossRefGoogle Scholar
  6. [6]
    Palis, J., Jr., de Melo, W., 1982, Geometric Dynamical Systems, (New York: Springer).zbMATHCrossRefGoogle Scholar
  7. [7]
    Sinai, Ya.G., 1989, Dynamical Systems, Vol. II, (New York: Springer).zbMATHGoogle Scholar
  8. [8]
    Wald, R.M., 1984, General Relativity, (Chicago: University of Chicago Press).zbMATHCrossRefGoogle Scholar
  9. [9]
    Sparrow, C., 1982, The Lorenz equations: bifurcations, chaos and strange attractors, Springer Lecture Notes in Math., Vol. 41.Google Scholar
  10. [10]
    Guckenheimer, J., Williams, R.F., 1979, “Structural stability of Lorenz attractors”, Publ. Math. IHES, 50, 59–72.MathSciNetzbMATHGoogle Scholar
  11. [11]
    Chrusciel, P.T., Isenberg, J., 1993, “On stability of differentiability of Cauchy horizons”, in preparation.Google Scholar
  12. [12]
    Friedman, J., Morris, M.S., Novikov, L, Echeverria, F., Glinkhammer, R., Thorne, K.S., Yurtsever, U., 1990, “Cauchy problem in spacetimes with closed timelike curves”, Phys. Rev., D 42, 1915–1930.ADSGoogle Scholar
  13. [13]
    Beem, J., Królak, A., 1993, “Causality and Cauchy horizons”, preprint.Google Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • P. T. Chruściel
    • 2
    • 3
  • J. Isenberg
    • 1
  1. 1.Department of Mathematics and Institute for Theoretical ScienceUniversity of OregonEugeneUSA
  2. 2.Max Planck Institut für AstrophysikGarching bei MünchenGermany
  3. 3.Institute of MathematicsPolish Academy of SciencesWarsawPoland

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