Chaos in a 3-body Self-Gravitating Cosmological Spacetime

Abstract

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.

arXiv comment40 pages, 16 figures, Latex

References in corpus (13)

• Exact Solution for the Metric and the Motion of Two Bodies in (1+1) Dimensional Gravity
• Exact Relativistic Two-Body Motion in Lineal Gravity
• Canonical reduction of two-dimensional gravity for Particle Dynamics
• Emergence of power-law correlation in 1-dimensional self-gravitating system
• Exact Solution for Relativistic Two-Body Motion in Dilaton Gravity
• Chaos in a Relativistic 3-body Self-Gravitating System
• Gravitation and Cosmology in Generalized (1+1)-dimensional dilaton gravity
• Exact Solutions to the Motion of Two Charged Particles in Lineal Gravity
• Exact Solutions of Relativistic Two-Body Motion in Lineal Gravity
• Chaos in an Exact Relativistic 3-body Self-Gravitating System
• 3-Body Dynamics in a (1+1) Dimensional Relativistic Self-Gravitating System
• Hierarchical clustering and formation of power-law correlation in 1-dimensional self-gravitating system
• The Linear Baryon

Cited by in corpus (1)

• One-Dimensional Relativistic Self-Gravitating Systems