Communications in Mathematical Physics

, Volume 150, Issue 2, pp 415–430 | Cite as

A nonintegrable model in general relativity

  • Richard Moeckel


The geodesic flow of a perturbation of the Schwarzschild metric is shown to possess a chaotic invariant set. The perturbed meric is a relativistic analogue of Hill's problem in classical celestial mechanics in that is models the effects of a distant third body.


Neural Network Statistical Physic General Relativity Complex System Nonlinear Dynamics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Hill] Hill, G.W.: Researches in the lunar theory. Am. J. Math.1, 5–26, 129–147, 245–260 (1878)Google Scholar
  2. [MTW] Minser, C., Thorn, K., Wheeler, J.: Gravitation. New York: W. H. Freeman 1973Google Scholar
  3. [O'Neill] O'Neill, B.: Semi-Riemannian geometry. New York: Academic Press 1983Google Scholar
  4. [Reg-Wh] Regge, T., Wheeler, J.: Stability of a Schwarzschild singularity. Phys. Rev.108 (4), 1063–1069 (1975)CrossRefGoogle Scholar
  5. [Rob] Robinson, C.: Horseschoes for autonomous Hamiltonian systems using the Melnikov integral. Ergodic Theory Dyn. Syst.8, 395–409 (1988)Google Scholar
  6. [Sch] Schutz, B.: A first course in general relativity. Cambridge: Camb. Univ. Press 1984Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Richard Moeckel
    • 1
  1. 1.Schol of MathematicsUniversity of MinnesotaMinneapolisUSA

Personalised recommendations