Chaos around charged black hole with dipoles

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.