Toward a definition of chaos for general relativity

TL;DR

This paper explores the challenge of defining chaos within general relativity, a theory distinguished by its diffeomorphism invariance, and presents initial results towards establishing an appropriate chaos definition.

Contribution

It introduces the need for a new chaos definition tailored to general relativity and offers preliminary results towards this development.

Findings

Identifies limitations of standard chaos definitions in general relativity

Proposes a framework for a chaos definition compatible with diffeomorphism invariance

Lays groundwork for future research in gravitational chaos

Abstract

General relativity exhibits a unique feature not represented in standard examples of chaotic systems; it is a spacetime diffeomorphism invariant theory. Thus many characterizations of chaos do not work. It is therefore necessary to develop a definition of chaos suitable for application to general relativity. This presentation will present results towards this goal.