Relativistic chaos is coordinate invariant

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.

4 pages, Revtex

References in corpus (5)

• The mixmaster universe: A chaotic Farey tale
• Chaos in the Einstein-Yang-Mills Equations
• Mixmaster chaos
• Chaos around a Hénon-Heiles-inspired exact perturbation of a black hole
• FRW cosmologies between chaos and integrability

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