Relativistic invariance of Lyapunov exponents in bounded and unbounded systems

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.