The 3-body problem for a relativistic self-gravitating linear system was studied. From the canonical formulation of linear gravity minimally coupled to three particles, an exact expression was obtained for the Hamiltonian, transcendentally expressed as a function of the four independent degrees of freedom. Based on this it was possible to solve for the motion of the system under arbitrary initial conditions and study quasiperiodic motion and chaos in a general-relativistic self-gravitating system.
Bibliographical noteFunding Information:
This work was supported by the Natural Sciences and Engineering Research Council of Canada.