Relativistic chaos is coordinate invariant

TL;DR

This paper demonstrates that chaos, as indicated by positive Lyapunov exponents, is coordinate invariant in general relativity, resolving previous misconceptions caused by noninvariance of Lyapunov exponents.

Contribution

It derives the transformation laws of Lyapunov exponents under general space-time transformations, proving chaos invariance in relativistic settings.

Findings

Lyapunov exponents transform according to specific laws under coordinate changes

Chaos is coordinate invariant when proper definitions are used

Previous claims of chaos noninvariance violate key assumptions

Abstract

The noninvariance of Lyapunov exponents in general relativity has led to the conclusion that chaos depends on the choice of the space-time coordinates. Strikingly, we uncover the transformation laws of Lyapunov exponents under general space-time transformations and we find that chaos, as characterized by positive Lyapunov exponents, is coordinate invariant. As a result, the previous conclusion regarding the noninvariance of chaos in cosmology, a major claim about chaos in general relativity, necessarily involves the violation of hypotheses required for a proper definition of the Lyapunov exponents.