Curvature and Chaos in General Relativity

Abstract

We clarify some points about the systems considered by Sota, Suzuki and Maeda in Class. Quantum Grav. 13, 1241 (1996). Contrary to the authors' claim for a non-homoclinic kind of chaos, we show the chaotic cases they considered are homoclinic in origin. The power of local criteria to predict chaos is once more questioned. We find that their local, curvature--based criterion is neither necessary nor sufficient for the occurrence of chaos. In fact, we argue that a merit of their search for local criteria applied to General Relativity is just to stress the weakness of locality itself, free of any pathologies related to the motion in effective Riemannian geometries.

8 pages, REVTEX, two postscript figures included, to appear in Class. Quantum Grav

References in corpus (4)

• Chaos in Static Axisymmetric Spacetimes I : Vacuum Case
• Chaos around a Hénon-Heiles-inspired exact perturbation of a black hole
• Geometry of chaos in the two-center problem in General Relativity
• Study of chaos in hamiltonian systems via convergent normal forms

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• Free motion around black holes with discs or rings: between integrability and chaos - I
• Signature of chaos in gravitational waves from a spinning particle
• Chaos in black holes surrounded by gravitational waves
• Chaotic motion in pp-wave spacetimes
• Free motion around black holes with discs or rings: between integrability and chaos -- V
• On the viability of local criteria for chaos
• On geometry of deformed black holes: II. Schwarzschild hole surrounded by a Bach-Weyl ring
• Chaos and Taub-NUT related spacetimes
• Chaotic motion in Kundt spacetimes