Computation of Lyapunov Exponents in General Relativity
Xin Wu, Tian-yi Huang
TL;DR
This paper introduces a new coordinate-invariant method for computing Lyapunov exponents in general relativity, enabling the analysis of chaos in curved spacetime systems.
Contribution
It proposes a novel definition and algorithm for relativistic Lyapunov exponents that are coordinate invariant in curved spacetime.
Findings
The new method is applicable in any coordinate system.
It accurately measures chaos in general relativistic systems.
The approach overcomes limitations of classical Lyapunov exponents in curved spacetime.
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.
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