Chaotic light scattering around extremal black holes

TL;DR

This paper demonstrates that light scattering around three or more extremal black holes exhibits chaos, with the complexity quantified by a lower bound on topological entropy, using classical Hamiltonian dynamics and symbolic dynamics techniques.

Contribution

It establishes the chaotic nature of light scattering in multi-black-hole systems and provides a quantitative lower bound on the topological entropy for such scenarios.

Findings

Chaotic scattering occurs for N ≥ 3 black holes.

Topological entropy has a lower bound of log(N-1).

Chaos is proven using symbolic dynamics and Hamiltonian reduction.

Abstract

We show that the scattering of light in the field of $N\geq 3$ 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 $N \geq 3$ black holes.