  The results of our study of the motion of a three particle, self-gravitating
system in general relativistic lineal gravity is presented for an arbitrary
ratio of the particle masses. We derive a canonical expression for the
Hamiltonian of the system and discuss the numerical solution of the resulting
equations of motion. This solution is compared to the corresponding
non-relativistic and post-Newtonian approximation solutions so that the
dynamics of the fully relativistic system can be interpretted as a correction
to the one-dimensional Newtonian self-gravitating system. We find that the
structure of the phase space of each of these systems yields a large variety of
interesting dynamics that can be divided into three distinct regions: annulus,
pretzel, and chaotic; the first two being regions of quasi-periodicity while
the latter is a region of chaos. By changing the relative masses of the three
particles we find that the relative sizes of these three phase space regions
changes and that this deformation can be interpreted physically in terms of the
gravitational interactions of the particles. Furthermore, we find that many of
the interesting characteristics found in the case where all of the particles
share the same mass also appears in our more general study. We find that there
are additional regions of chaos in the unequal mass system which are not
present in the equal mass case. We compare these results to those found in
similar systems.
