Chaotic Scattering and Capture of Strings by Black Hole

TL;DR

This paper investigates the chaotic behavior in the scattering and capture of cosmic strings by a black hole, revealing fractal structures and transitions from order to chaos.

Contribution

It demonstrates the presence of fractal basin boundaries and unstable periodic solutions in cosmic string-black hole interactions, analyzing how chaos emerges with energy variations.

Findings

Fractal dimension of basin boundaries varies with energy.

Existence of a strange repellor in string scattering.

Transition from ordered to chaotic dynamics as energy increases.

Abstract

We consider scattering and capture of circular cosmic strings by a Schwarzschild black hole. Although being a priori a very simple axially symmetric two-body problem, it shows all the features of chaotic scattering. In particular, it contains a fractal set of unstable periodic solutions; a so-called strange repellor. We study the different types of trajectories and obtain the fractal dimension of the basin-boundary separating the space of initial conditions according to the different asymptotic outcomes. We also consider the fractal dimension as a function of energy, and discuss the transition from order to chaos.