Chaos and fractals around black holes

Feb, 1995
21 pages
Published in:
  • Fractals 3 (1995) 01, 161-181
  • Published: Mar, 1995
e-Print:
Report number:
  • UTPT-94-22,
  • UM-P-94-87

Citations per year

19952002200920162023012345
Abstract: (WSP)
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.
Note:
  • To appear in "Fractals" March issue (World Scientific), 20 figures available by request, also available from SLAC's gr-qc postscript archive