Relativistic Chaos is Coordinate Invariant

Phys. Rev. Lett. 91, 231101 – Published 4 December 2003
Adilson E. Motter


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.


  • Received 5 May 2003
  • Published 4 December 2003

© 2003 The American Physical Society

Authors & Affiliations

Adilson E. Motter*

  • Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany

  • *Electronic address:

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