Spinning compact object and chaos in galactic centres

¹ Department of Physics, St. Xavier’s College (Autonomous), Kolkata - 700016, India
² School of Physics and Astronomy, Cardiff University, Cardiff CF24 3AA, Wales
³ Department of Physics, Raja Peary Mohan College, Hooghly - 712258, India

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 29 May 2026

Abstract

Galactic centres are extremely complex environments, formed primarily of a supermassive black hole (SMBH), which is surrounded by asymmetric mass distributions comprised of nuclear star clusters (NSC), molecular gas, etc forming disks or halos. These elements together exert a gravitational field, which, combined with relativistic corrections from the spin of the SMBH generate strong nonlinear dynamics and chaotic orbits. We model this region using a multipolar expansion potential [1], where the central compact object is denoted by the Artemova-Björnsson-Novikov pseudo-Newtonian potential, which mimics the spin dependence of a Kerr-like BH. The surrounding halo is modelled as an axisymmetric, shell-like mass distribution expanded to the dipole order to induce asymmetry. Previous works have mostly quantified the chaos caused by the BH spin and dipole moment using Poincaré sections, SALI [2] and other such chaos indicators. In this study, we incorporate stability analysis and basins of attraction to provide a global approach to understanding the dynamics of the system. Stability analysis around fixed points gives a deeper context on the local behaviour, while basins of convergence showcase sensitivity to initial conditions and reveal fractal boundaries. Our results show that the BH spin highly reconstructs the equilibrium landscape. Depending on its magnitude and orientation, it can either intensify the chaos induced by the halo asymmetry or simplify the phase space. These discoveries broadly impact our understanding of how relativistic spin effects and multipole moments collectively affect particle motion in galactic centres.