Chaotic behavior of geodesics in Kerr-like spacetime

Abstract

In recent years, experimental and theoretical research on the nature of supermassive bodies that inhabit the central regions of galaxies has grown significantly. In this contribution, we study the motion of unitary mass test particles in a perturbed Kerr-like metric. The metric represents the approximate exterior spacetime of a massive rotating body with mass quadrupole moment $q$. Through extensive study of the geodesics, it is found that the chaotic behavior proliferates as the $q$ parameter increases. Several structures are found in the phase space, such as Birkhoff chains of islands and hyperbolic points if $q\ensuremath{\ne}0$. Additionally, chaotic regions crossing the null radial momentum axis (${p}_{r}=0$) are studied by analyzing the rotation number, and several islands of stability are found that are preserved as the deformation of the rotating body increases, while others are destroyed. Furthermore, chaotic behavior is found to be dictated by stickiness, chaotic orbits that remain attached to stable ones for a long time before they become divergent and are attracted to the event horizon.