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

TL;DR

This paper investigates how particle dynamics around black holes with anisotropic matter fields can violate the chaos bound, showing that higher angular momentum and anisotropic matter increase this violation, with implications for understanding chaos in gravitational systems.

Contribution

It demonstrates the violation of the chaos bound in black hole spacetimes with anisotropic matter fields and analyzes the influence of angular momentum and matter anisotropy on this violation.

Findings

Violations of the chaos bound increase with higher angular momentum.

Anisotropic matter fields further promote chaos bound violations.

Geodesic motion can be integrable using Hamiltonian-Jacobi formalism.

Abstract

We study the homoclinic orbit and the violation of chaos bound, which are obtained by particle motions around a black hole that coexist with anisotropic matter fields. The homoclinic one is associated with an unstable local maximum of the effective potential. By perturbing a particle located slightly away from the homoclinic one, we numerically compute Lyapunov exponents indicating the sensitivity of the initial value. Our results demonstrate that the violation of the chaos bound increases with higher angular momentum, and the anisotropic matter gives rise to violating the chaos bound further, even in the case of the nonextremal black hole. We utilize the Hamiltonian-Jacobi formalism to explicitly illustrate how the geodesic motion of a particle can be integrable in the procedure of obtaining our findings.