Computation of Lyapunov Exponents in General Relativity
General Relativity and Quantum Cosmology
2009-11-10 v2
Abstract
Lyapunov exponents (LEs) are key indicators of chaos in dynamical systems. In general relativity the classical definition of LE meets difficulty because it is not coordinate invariant and spacetime coordinates lose their physical meaning as in Newtonian dynamics. We propose a new definition of relativistic LE and give its algorithm in any coordinate system, which represents the observed changing law of the space separation between two neighboring particles (an 'observer' and a 'neighbor'), and is truly coordinate invariant in a curved spacetime.
Cite
@article{arxiv.gr-qc/0302118,
title = {Computation of Lyapunov Exponents in General Relativity},
author = {Xin Wu and Tian-yi Huang},
journal= {arXiv preprint arXiv:gr-qc/0302118},
year = {2009}
}
Comments
13 pages, 3 figures