Curvature and Chaos in General Relativity

TL;DR

This paper critiques previous claims about chaos in certain general relativity systems, demonstrating that the considered chaos is homoclinic and questioning the effectiveness of local curvature-based criteria for predicting chaos.

Contribution

It clarifies the nature of chaos in the studied systems and challenges the reliability of local curvature criteria in predicting chaos in general relativity.

Findings

Chaotic cases are homoclinic in origin.

Local curvature criteria are neither necessary nor sufficient for chaos.

Highlights the limitations of local criteria 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.