PMID: 15244709Jul 13, 2004Paper

Three-body dynamics in a (1+1) -dimensional relativistic self-gravitating system

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
J J Malecki, R B Mann

Abstract

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 nonrelativistic and post-Newtonian approximation solutions so that the dynamics of the fully relativistic system can be interpreted 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 quasiperiodicity 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 ap...Continue Reading

References

Jul 15, 1990·Physical Review. a·N D WhelanJ K Cannizzo
Feb 28, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·R B Mann, P Chak
Apr 12, 2003·Physical Review Letters·F BurnellT Ohta
Apr 1, 1993·Chaos·Jarmo Hietarinta, Seppo Mikkola
Mar 5, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·F BurnellT Ohta

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