Chaotic exits from a weakly magnetized Schwarzschild black hole

TL;DR

This paper investigates the chaotic dynamics of charged particles around a weakly magnetized Schwarzschild black hole, revealing complex basin structures and how magnetic strength influences escape behavior.

Contribution

It provides a detailed numerical analysis of basin structures, discovers the Wada property in the basins, and derives an approximate analytic expression for escape energy.

Findings

Basin boundaries exhibit Wada property.

Uncertainty in final state prediction increases with magnetic strength.

Derived an approximate formula for critical escape energy.

Abstract

A charged particle kicked from an initial circular orbit around a weakly magnetized Schwarzschild black hole undergoes transient chaotic motion before either getting captured by the black hole or escaping upstream or downstream with respect to the direction of the magnetic field. These final states form basins of attraction in the space of initial states. We provide a detailed numerical study of the basin structure of this initial state space. We find it to possess the peculiar Wada property: each of its basin boundaries is shared by all three basins. Using basin entropy as a measure, we show that uncertainty in predicting the final exit state increases with stronger magnetic interaction. We also present an approximate analytic expression of the critical escape energy for a vertically-kicked charged particle, and discuss how this depends on the strength of the magnetic interaction.