Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2010-06-28
Phys.Rev.D74:083001,2006
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
12 pages, 5 figures
Scientific paper
10.1103/PhysRevD.74.083001
We compare three methods for computing invariant Lyapunov exponents (LEs) in general relativity. They involve the geodesic deviation vector technique (M1), the two-nearby-orbits method with projection operations and with coordinate time as an independent variable (M2), and the two-nearby-orbits method without projection operations and with proper time as an independent variable (M3). An analysis indicates that M1 and M3 do not need any projection operation. In general, the values of LEs from the three methods are almost the same. As an advantage, M3 is simpler to use than M2. In addition, we propose to construct the invariant fast Lyapunov indictor (FLI) with two-nearby-trajectories and give its algorithm in order to quickly distinguish chaos from order. Taking a static axisymmetric spacetime as a physical model, we apply the invariant FLIs to explore the global dynamics of phase space of the system where regions of chaos and order are clearlyidentified.
Huang Tian-Yi
Wu Xin
Zhang Hong
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