Chaotic motion in multi-black hole spacetimes and holographic screens

We investigate the geodesic motion in $D-$dimensional Majumdar-Papapetrou multi-black hole spacetimes and find that the qualitative features of the D=4 case are shared by the higher dimensional configurations. The motion of timelike and null particles is chaotic, the phase space being divided into basins of attraction which are separated by a fractal boundary, with a fractal dimension $d_B$. The mapping of the geodesic trajectories on a screen placed in the asymptotic region is also investigated. We find that the fractal properties of the phase space induces a fractal structure on the holographic screen, with a fractal dimension $d_B-1$.