Chaos in a Relativistic 3-body Self-Gravitating System

Details Chaos in a Relativistic 3-body Self-Gravitating System Chaos in a Relativistic 3-body Self-Gravitating System

2002-08-16

arxiv.org/abs/gr-qc/0208044v3

Phys.Rev.Lett. 90 (2003) 134101

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages, LaTex, 3 figures, final version to appear in Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.90.134101

We consider the 3-body problem in relativistic lineal gravity and obtain an exact expression for its Hamiltonian and equations of motion. While general-relativistic effects yield more tightly-bound orbits of higher frequency compared to their non-relativistic counterparts, as energy increases we find in the equal-mass case no evidence for either global chaos or a breakdown from regular to chaotic motion, despite the high degree of non-linearity in the system. We find numerical evidence for a countably infinite class of non-chaotic orbits, yielding a fractal structure in the outer regions of the Poincare plot.

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