Chaos around charged black hole with dipoles

TL;DR

This paper explores the chaotic behavior of test particles around charged black holes with dipoles, revealing how potential well structures influence orbital stability and chaos through numerical simulations and phase space analysis.

Contribution

It provides a detailed analysis of how dipole-induced potential structures lead to chaos in particle orbits near charged black holes, using numerical and phase space methods.

Findings

Potential curves exhibit one or three wells depending on parameters.

Chaotic motion arises mainly from black hole dipoles.

Orbits show sensitive dependence on initial conditions.

Abstract

We investigated dynamics of the test particle in the gravitational field of the charged black hole with dipoles in this paper. At first we have studied the gravitational potential, by the numerical simulations, we found, for appropriate parameters, that there are two different cases in the potential curve, one is a well case with a stable critical point, and the other is three wells case with three stable critical points and two unstable critical points. As consequence, the chaotic motion will rise. We have performed the evolution of the orbits of the test particle in phase space, we found that the orbits of the test particle randomly oscillate without any periods, even sensitively depend on the initial conditions and parameters. By performing Poincar\'{e} sections for different values of the parameters and initial condition, we have found regular motion and chaotic motion. By comparing these Poincar\'{e} sections, we further conformed that the chaotic motion of the test particle mainly origins from the dipoles of the black hole.