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Chaos in a Relativistic 3-body Self-Gravitating System

F. J. Burnell·R. B. Mann·T. Ohta
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Abstract

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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F. J. Burnell, R. B. Mann, T. Ohta. 2003-03-03. Chaos in a Relativistic 3-body Self-Gravitating System. https://doi.org/10.1103/physrevlett.90.134101

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