CHAOS AND FRACTALS AROUND BLACK-HOLES

Fractal basin boundaries provide an important means of characterizing chaotic systems. We apply these ideas to general relativity, where oth er properties such as Lyapunov exponents are difficult to define in an observer independent manner. Here we discuss the difficulties in desc ribing chaotic systems in general relativity and investigate the motio n of particles in two and three black hole spacetimes. We show that th e dynamics is chaotic by exhibiting the basins of attraction of the bl ack holes which have fractal boundaries. Overcoming problems of princi ple as well as numerical difficulties, we evaluate Lyapunov exponents numerically and find that some trajectories have a positive exponent.