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.
- Publication:
-
Physical Review Letters
- Pub Date:
- December 2003
- DOI:
- 10.1103/PhysRevLett.91.231101
- arXiv:
- arXiv:gr-qc/0305020
- Bibcode:
- 2003PhRvL..91w1101M
- Keywords:
-
- 98.80.Jk;
- 04.20.-q;
- 05.45.-a;
- Mathematical and relativistic aspects of cosmology;
- Classical general relativity;
- Nonlinear dynamics and chaos;
- Astrophysics;
- General Relativity and Quantum Cosmology
- E-Print:
- 4 pages, Revtex