Homoclinic orbit and the violation of chaos bound around the black hole with anisotropic matter fields

Abstract

We study the Homoclinic orbit and the violation of chaos bound. They are by particle motions around the black hole that coexist with anisotropic matter fields. The homoclinic one is related to the existence of an unstable local maximum of the effective potential. When we perturbed a particle given at a position located a bit far away from that of a particle in this orbit, we numerically compute Lyapunov exponents indicating the sensitivity of the initial value. We show that the violation of the chaos bound increases with increasing angular momentum, and the anisotropic matter gives rise to violating the chaos bound further, even in the case of the non-extremal black hole.