Relativistic Effects on Triple Black Holes II: The Influence of Spin in Burrau's Problem

We continue our study of triple systems of black holes in the context of Burrau's problem by including the effect of spin. For a more general study we also include a study of the phase space in Agekian-Anosova region. This was done via numerical integration of orbits with ARCcode which uses relativistic corrections (post-Newtonian) up to the 2.5$^{th}$ order. For the Agekian-Anosova region we study black holes with mass unit 10$^{6}$ M$_{\odot}$ and allow one of the black holes to be maximally rotating. The same configurations were tested without the inclusion of spin and we found that simulations that varied greatly from the spin to no spin cases had much closer approaches between one of the Schwarzschild black holes and the Kerr black hole. In the context of Burrau's problem, Pythagorean triangles with different linear scales were selected where the largest black hole in these systems were given spin vectors in normalised units where maximum is close to unity, ranging from 0 to about 0.95. Mass unit was also varied between 10$^{0}$ M$_{\odot}$ - 10$^{12}$ M$_{\odot}$. It was found that while there was no distinctive effect on the number of two-body encounters nor the fraction of mergers, the lifetimes of the systems may have been affected - particularly in the intermediary mass ranges (10$^{4}$ M$_{\odot}$-10$^{7}$ M$_{\odot}$) in comparison to the zero spin problem. Systems also ended up moving from the two-dimensional to three-dimensional where we see increased motion in the z-axis with increasing spin magnitude for the large mass systems.