Chaotic dynamics of off-equatorial orbits around pseudo-Newtonian compact objects with dipolar halos

In this paper, we implement a generalised pseudo-Newtonian potential to study the off-equatorial orbits inclined at a certain angle with the equatorial plane around Schwarzschild and Kerr-like compact object primaries surrounded by a dipolar halo of matter. The chaotic dynamics of the orbits are detailed for both non-relativistic and special-relativistic test particles. The dependence of the degree of chaos on the Kerr parameter $a$ and the inclination angle $i$ is established individually using widely used indicators, such as the Poincaré Maps and the Maximum Lyapunov Exponents. Although the orbits' chaoticity has a positive correlation with $i$, the growth in the chaotic behaviour is not systematic. There is a threshold value of the inclination angle $i_{\text{c}}$, after which the degree of chaos sharply increases. On the other hand, the chaoticity of the inclined orbits anti-correlates with $a$ throughout its entire range. However, the negative correlation is systematic at lower values of the inclination angle. At higher values of $i$, the degree of chaos increases rapidly below a threshold value of the Kerr parameter, $a_{\text{c}}$. Above this threshold value, the correlation becomes weak. Furthermore, we establish a qualitative correlation between the threshold values and the overall chaoticity of the system. The studies performed with different orbital parameters and several initial conditions reveal the intricate nature of the system.

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