Advertisement

Communications in Mathematical Physics

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

A nonintegrable model in general relativity

  • Richard Moeckel
Article

Abstract

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.

Keywords

Neural Network Statistical Physic General Relativity Complex System Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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