Chaos in a Relativistic 3-body Self-Gravitating System

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.

arXiv comment9 pages, LaTex, 3 figures, final version to appear in Phys. Rev. Lett

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• Exact Relativistic Two-Body Motion in Lineal Gravity
• Canonical reduction of two-dimensional gravity for Particle Dynamics
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• 3-Body Dynamics in a (1+1) Dimensional Relativistic Self-Gravitating System
• Perturbative Quantum Gravity Coupled to Particles in (1+1)-Dimensions
• One-Dimensional Relativistic Self-Gravitating Systems
• Chaos in a 3-body Self-Gravitating Cosmological Spacetime
• Dynamics of Coulombic and Gravitational Periodic Systems
• Dynamical Charged N-body Equilibrium in Circular Dilaton Gravity
• Non-linearity and chaos in the kicked top
• Detecting Irregular Orbits in Gravitational N-body Simulations