Chaotic behavior in a charged three-body self-gravitating system

Abstract

We investigate the equal-mass three-body charged system in general relativistic lineal gravity. The electric properties of the charged particles along with the gravitational self-attraction of the bodies introduce features that do not have a nonrelativistic counterpart. We derive a canonical expression for the Hamiltonian of the system and discuss the numerical solution of the resulting equations of motion. We consider various combinations of charges and find that the structure of the phase space yields a rich variety of interesting dynamics that can be divided into three distinct regions: annulus, pretzel, and chaotic; the first two are regions of quasiperiodicity while the latter is a region of chaos. When the charge configuration is repulsive the amount of chaos is enhanced relative to that of the neutral case ͑leading to Kolmogorov-Arnold-Moser breakdown͒, whereas the chaos is only enhanced throughout a band between the annulus and pretzel regions with a significant development of pretzel areas for attractive configurations when two charges have opposite signs. We find a new class of chaotic orbits that are of hourglass shape in the hexagonal representation of the three-body motion.