Time and Chaos in General Relativity

TL;DR

This paper introduces invariant measures for chaos in general relativity, enabling coordinate-independent analysis, and applies these methods to demonstrate transient soft chaos in Mixmaster universes.

Contribution

It presents new invariant measures for chaos in relativity and shows how to relate them to standard measures through preferred time choices.

Findings

Invariant measures successfully quantify chaos in relativistic systems.

Mixmaster universes exhibit transient soft chaos.

Coordinate-independent measures align with traditional chaos indicators.

Abstract

The study of dynamics in general relativity has been hampered by a lack of coordinate independent measures of chaos. Here we present a variety of invariant measures for quantifying chaotic dynamics in relativity by exploiting the coordinate independence of fractal dimensions. We discuss how preferred choices of time naturally arise in chaotic systems and how the existence of invariant signals of chaos allow us to reinstate standard coordinate dependent measures. As an application, we study the Mixmaster universes and find it to exhibit transient soft chaos.