Astronomy and Astrophysics – Astrophysics
Scientific paper
2006-07-05
Phys.Rev.D76:104051,2007
Astronomy and Astrophysics
Astrophysics
40 pages, 16 figures, Latex
Scientific paper
10.1103/PhysRevD.76.104051
We investigate the equal-mass 3-body system in general relativistic lineal gravity in the presence of a cosmological constant $\Lambda$. The cosmological vacuum energy introduces features that do not have a non-relativistic counterpart, inducing a competing expansion/contraction of spacetime that competes with the gravitational self-attraction of the bodies. We derive a canonical expression for the Hamiltonian of the system and discuss the numerical solution of the resulting equations of motion. As for the system with $\Lambda=0$, we 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 being regions of quasi-periodicity while the latter is a region of chaos. However unlike the $\Lambda=0$ case, we find that a negative cosmological constant considerably diminishes the amount of chaos in the system, even beyond that of the $\Lambda=0$ non-relativistic system. By contrast, a positive cosmological constant considerably enhances the amount of chaos, typically leading to KAM breakdown.
Koop Michael J.
Mann Robert B.
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