Computation of Lyapunov Exponents in General Relativity

Details Computation of Lyapunov Exponents in General Relativity Computation of Lyapunov Exponents in General Relativity

2003-02-28

arxiv.org/abs/gr-qc/0302118v2

Phys.Lett. A313 (2003) 77-81

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, 3 figures

Scientific paper

10.1016/S0375-9601(03)00720-5

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.

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