Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1995-02-06
Fractals 3 (1995) 161
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
To appear in "Fractals" March issue (World Scientific), 20 figures available by request, also available from SLAC's gr-qc post
Scientific paper
Fractal basin boundaries provide an important means of characterizing chaotic systems. We apply these ideas to general relativity, where other properties such as Lyapunov exponents are difficult to define in an observer independent manner. Here we discuss the difficulties in describing chaotic systems in general relativity and investigate the motion of particles in two- and three-black-hole spacetimes. We show that the dynamics is chaotic by exhibiting the basins of attraction of the black holes which have fractal boundaries. Overcoming problems of principle as well as numerical difficulties, we evaluate Lyapunov exponents numerically and find that some trajectories have a positive exponent.
Cornish Neil
Dettmann Carl
Frankel Norm
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