Chaos around a H\'enon-Heiles-inspired exact perturbation of a black hole

TL;DR

This paper presents an exact solution to Einstein's equations combining a Schwarzschild black hole with multipolar halo terms, demonstrating chaotic orbital behavior analogous to the Hénon-Heiles system in the Newtonian limit.

Contribution

It introduces a novel exact solution modeling a black hole with a multipolar halo and analyzes the resulting chaotic orbital dynamics.

Findings

Bounded zones of chaos around the black hole are identified.

The solution reduces to a Hénon-Heiles-like potential in the Newtonian limit.

Abstract

A solution of the Einstein's equations that represents the superposition of a Schwarszchild black hole with both quadrupolar and octopolar terms describing a halo is exhibited. We show that this solution, in the Newtonian limit, is an analog to the well known H\'enon-Heiles potential. The integrability of orbits of test particles moving around a black hole representing the galactic center is studied and bounded zones of chaotic behavior are found.