Chaotic light scattering around extremal black holes

Abstract

We show that the scattering of light in the field of Nge 3 static extremal black holes is chaotic in the planar case. The relativistic dynamics of such extremal objects reduce to that of a classical Hamiltonian system. Certain values of the dilaton coupling then allow one to apply techniques from symbolic dynamics and classical potential scattering. This results in a lower bound on the topological entropy of order log (N-1), thus proving the emergence of chaotic scattering for N ge 3 black holes.