http://arxiv.org/abs/2303.14740
In this paper, we implement a generalized pseudo-Newtonian potential and prescribe a numerical fitting formalism, to study the off-equatorial orbits inclined at a certain angle with the equatorial plane around both 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 rotation parameter $a$ and the inclination angle $i$ is established individually using widely used indicators, such as the Poincar\’e Map and the Lyapunov Characteristic Number. We find that although the chaoticity of the orbits has a positive correlation with $i$, the growth in the chaotic behaviour is not systematic. There exists a threshold value of the inclination angle $i_{\text{c}}$, after which the degree of chaos shows a sharp increase. On the other hand, the chaoticity of the inclined orbits anti-correlates with $a$ at the lower inclination angles. At higher values of $i$, the degree of chaos is maximum for the maximally counter-rotating compact objects, though it has a weak negative, sometimes positive, correlation with $a$ at its higher values. The studies performed with several initial conditions and orbital parameters reveal the intricate nature of the system.
S. Das and S. Roychowdhury
Tue, 28 Mar 23
49/81
Comments: 17 pages, 14 figures