Relativistic invariance of Lyapunov exponents in bounded and unbounded systems

TL;DR

This paper develops a framework to analyze how Lyapunov exponents, indicators of chaos, transform under relativistic changes of reference frames, ensuring observer-independent chaos characterization in bounded and unbounded systems.

Contribution

It introduces a general approach to overcome observer dependence of Lyapunov exponents in relativistic systems, clarifying their transformation properties under Lorentz, Rindler, and rotating frame transformations.

Findings

Inertial and rotating observers agree on chaos characterization via LEs.

The transformation of LEs under Lorentz boosts is well-defined.

Event horizons affect the interpretation of LEs for accelerated observers.

Abstract

The study of chaos in relativistic systems has been hampered by the observer dependence of Lyapunov exponents (LEs) and of conditions, such as orbit boundedness, invoked in the interpretation of LEs as indicators of chaos. Here we establish a general framework that overcomes both difficulties and apply the resulting approach to address three fundamental questions: how LEs transform under Lorentz and Rindler transformations and under transformations to uniformly rotating frames. The answers to the first and third questions show that inertial and uniformly rotating observers agree on a characterization of chaos based on LEs. The second question, on the other hand, is an ill-posed problem due to the event horizons inherent to uniformly accelerated observers.