Exploring Chaotic Motion of a Particle in the Centre of a Galaxy with a Prolate Halo

Uditi Nag; Yeasin Ali; Suparna Roychowdhury

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arXiv · 2601.05760

Exploring Chaotic Motion of a Particle in the Centre of a Galaxy with a Prolate Halo

Uditi Nag·Yeasin Ali·Suparna Roychowdhury

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Abstract

The majority of galaxies are known to have supermassive black holes (SMBHs) at their core, which have a tremendous gravitational pull on the objects around them. When embedded within extended matter distributions such as prolate, shell-like halos, they give rise to complex gravitational fields that often drive nearby particles into chaotic orbits. The inherently nonlinear nature of such motion, shaped by general relativity, makes direct analysis highly challenging. To overcome this, pseudo-Newtonian potentials are used to approximate relativistic effects within a Newtonian framework. In this study, we model the central SMBH using the Artemova-Bjornsson-Novikov (1996) potential to mimic the rotational effects of a Kerr-like black hole. The surrounding prolate halo is treated as an axisymmetric, shell-like mass distribution, represented through a multipole expansion including dipole and quadrupole components. Poincare sections and the Maximum Lyapunov Exponent (MLE) reveal how the SMBH-halo system drives both order and chaos, with the SMBH spin modulating the dynamics by enhancing or suppressing chaos depending on its direction and magnitude.

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Uditi Nag, Yeasin Ali, Suparna Roychowdhury. 2026-01-09. Exploring Chaotic Motion of a Particle in the Centre of a Galaxy with a Prolate Halo. https://arxiv.org/abs/2601.05760

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